You don't even need to be a software developer to understand. Chefs working with limited kitchen space is a good enough example of this. The most important thing is that there needs to be an adequate amount of work for each person to work efficiently. Software development has plenty logistical implications that come from bigger teams.
+Nathan How so? I think people understand when a larger team is needed for a task, and when a task can be done by a smaller team. It's mainly just common sense. Having too many people on a simple task just wastes man hours (which are expensive). Conversely, having too few people on a big task however risks you not meeting deadlines. Again to use food as an example. A waiter knows what it's like to both be over-staffed and under-staffed. This saying is not a religious belief. The saying arose because of observations.
I know this is a math problem and all, but everything I've seen in many different jobs tells me that Bob and Charlie should get out of the way so Alice can fix everything, so they can all go home.
What if Charlie upped the quality significantly at a deeper level of analysis, while the cooperation among the three allowed it to be completed at 9 minutes less? yeet
My thinking "Bob is irrelevant, Charlie sucks, the time will be equal to the amount of time it takes for Alice and Charlie, so 3 hours." While I was technically wrong, I feel my answer falls within the spectrum of likely real world outcomes.
I'm surprised that Bob would agree to work with Charlie again, seeing as he has to spend twice as long at work if he is paired with Charlie, compared with when he is paired with Alice.
Problem kind of ignores diminishing returns. Picture three people working in a 5X8 foot bathroom, one painting, another installing a new supply and faucet to the sink, and the third putting in a shower surround. Total job will get done faster if they work on their individual part at different times. Also, yeah, Charlie should be fired, and from the look of the times Alice might deserve a raise.
Naihonn I have lived a few years and my experience is the less capable you are. The better job you get. Stop trying so hard. Life is easier than you think.
I thought about it a little differently than the 'percentage' system. I thought of them as rates. Alice works at 'a' jobs per hour, Bob at 'b' jobs per hour, Charlie at 'c' jobs per hour. Adding their rates together, Alice and Bob would work at the rate of 1 job per 2 hours, so the equation is A + B = 1/2, with the units being 1 job / 2 hours. So you'd get: A + B = 1/2 A + C = 1/3 B + C = 1/4 Using the neat little trick and adding all of them together, you get 2A + 2B + 2C = 1/2 + 1/3 + 1/4 2(A + B + C) = 6/12 + 4/12 + 3/12 A + B + C = 13/24 All of them together can work at the rate of 13 jobs per 24 hours, and if you want to know how long it takes them to complete 1 job, just invert the answer: 24/13 ≈ 1.85 hrs. Charlie needs to step his game up.
This is the way I did it. You quickly see that you have to deal with rates due to all working simultaneously. The wrong answer of 4.5 is actually correct if A, B, and C have to work sequentially and not in parallel.
my brain immediately went “well alice and bob are still part of the group so it’s still 2 hours because they would just ignore charlie since he’d be slowing them down”
I have 20 years working as an engineer. After i solve any problem, I always apply a common sense check. This is something i see most beginning engineers skip and it causes them to not catch most of their errors until the errors have culminated into an obvious failure.
It's one of the most powerful aspects of math, that there is OFTEN PLENTY of common-sense checking of things, to help reduce human error significantly. The fact that massive amounts of college students now apparently have NO CLUE about this says it ALL, re the state of the modern education system (in the US, anyway), IMO.
"A common mistake is that students turn the names into variables and turn the sentences into equations..." * quietly crumples paper before shoving it into my mouth *
Yup - in my experience if you have 2 people wo are really good at their job (like Bob and Alice clearly are) and you add a third worker who is a dog... the first answer is probably more accurate.
Charlies average is actually closer to Alice's according to the information given. I came up with 4 hours with all 3 of them working to gather. I dont disagree with the fact that working with Charlie wouldnt be the most efficient.
charlie calls them both racist and spends 6 hours in the h/r dept attempting to get the other two fired alice spends 5 hours in h/r with a claim of sexual harassment on both bob and charlie says she wants a raise and promotion and bob spends 5 min dropping off a i quit notice at h/r because he is sick of working with either of them lol
That is the logical conclusion . Charlie can stop others from interrupting the work or "trying to help" . .My first thought was Alice can do it in an hour by herself .
I have been in management for over 25 years. This is what I can see from this problem in the real world. 1: Bob and Charlie are friends. This explains why the task takes longer when it is only the 2 of them. 2: Bob is the harder worker between Bob and Charlie. It takes longer for Charlie and Alice to complete the task. 3: Neither Bob nor Charlie likes working with Alice. Both Bob and Charlie take less time to complete the task when working with Alice than when they work together. 4: The "wrong" equation is most likely accurate in the given scenario. When all 3 are working together, Bob and Charlie will spend most of their time talking and goofing off. Poor Alice will have to do most of the work. Therefore, it will take longer, with 2 of the 3 not working and spending more time playing grab-ass with each other.
The job will never be completed. Alice, Charlie and Bob have been working on this same job since I was in school. If they haven’t finished it by now, they never will.
The real answer is 4.5 hours. Alice, Bob, and Charlie are good friends who enjoy each other's company, so when they are working on a task together, it takes longer.
This solution is easier for me: Change hours per work into work per hour (wph for convenience) to get A + B = 1/2 A + C = 1/3 B + C = 1/4 Now solve: A - B = 4/12 - 3/12 A = B + 1/12 B + 1/12 + B = 1/2 2B = 5/12 B = 5/24 A = 5/24 + 1/12 = 7/24 C = 1/4 - B = 6/24 - 5/24 = 1/24 Now consider 7/24 + 5/24 + 1/24 = 13/24 wph 1/(13/24 wph) = 24/13 hpw They are doing 1 work, so (24/13 hpw) * (1work) = 24/13 hours
"To the professors' surprise, many of the students set up the wrong equations and could not solve this problem" -- This is a fairy tale. No professor would be surprised by that.
Actually, the professor would count them all wrong. The professor would say the correct set up would be to let the government do the task while the 3 workers where on the draw from the government!!
... nor would a professor be surprised that they turned in the resulting (wrong) answer. A more intersting question is: of those who turned in the wrong answer, how many knew it was wrong vs how many didn't even think about it. A follow up question is: of those who knew it was wrong, how many of them actually felt some kind of remorse (as opposed to those who were perfectly content to have something mathy-looking on paper.) Sorry, Mr. Talwalker, but in my experience, concern for the rectitude of one's math homework was non-existent among almost all of my peers -- even at the college level (and even at a highly respected science and engineering school, no less!) My contemporaries were masters at playing to the curve. They'd've seen this problem as a quickie free-bee and moved on as fast as possible.
Honestly I think most find the wrong answer and knew it was wrong, they just had no idea how to do it right. At least that was me. I only didn't bother to do equations
I got a really close answer using the incorrect method; I did the incorrect variable assignment but set up a final equation A x B x C instead of A + B + C and I got 1.875 hours or 1 hour 52 minutes 30 seconds. Really close
@@waelnawwal it depends on reasoning tho. The wrong method makes no sense at all, even if it cn be described using words. Dw im also a victim of this problem
The funny thing about questions like these is people always go: "It wouldn't make sense for more people to work on a task and have it take longer." My response is always, "Clearly you have never managed employees."
Even ignoring the social psychology issues, most tasks are restricted physically or logistically in how many people can effectively work on them. 3 people can't wash dishes in a single sink, for example. The math problem assumes a very particular sort of task.
I found the manager that sits on his/her ass all day and has no idea how to actually do the job or even tie their own shoes for that matter. Plugging in names on a schedule and entering fields on a payroll application is so hard, isnt it?
Here’s my solution: Bob and Charlie must be dating, so they’re the most distracted when they work together because they’re all lovey-dovey, which is why it takes them 4 hours to finish the job. Alice and Charlie are close siblings, so they waste an hour or so talking while working together. Alice and Bob don’t really know each other well, so they’re able to focus more and finish the job in 2 hours. If all three of them were to work together, then Alice will realize that Charlie and Bob are dating, and she’ll start being very protective of Charlie because she doesn’t trust Bob with him (she’s an overprotective older sister and doesn’t know Bob very well). This will lead to an argument that results in bruised feelings, potentially damaged relationships, and no work done. So they never finish the job. I’ll take my Nobel Prize now, thaaank you :D
After that Bob’s friends Daniel and Ethan come in and start fighting and now their relationship is broken which results in stress-working, and now the technical work/h is actually higher. They are now working separate jobs with efficiency. Now the work per hour is higher than Alice, who is sobbing in the corner.
@@EMLtheViewer Good evening Mr. Emalan. I am almost a scientist. I am a Ph.D. A Doctor in the fields of Management and Psychology. Nice to meet you. :)
So funny but the wrong initial answer is probably the most accurate. When doing construction In a limited area, more people can just complicate things.
In india we are always taught to calculate using 1 hour's work i.e the work done in 1 hour which is in this case is 1/2, 1/3, 1/4 respectively. I did it this way and got the answer correctly. Now seeing your video it makes sense why we used to take 1 hour's work instead of the actual time taken. Thanks folk! 🙂 However you have to do the reciprocal of the answer obtained in order to get the time because it's just the part of work all three could do in an hour.
Work rate per hour for the individual persons: Alice: 7/24, so she would perform the task in 3 and a half hours. Bob: 5/24, so he would perform the task in slightly less than 5 hours. Charlie: 1/24, so he would perform the task in 24 hours.
So Alice deserves a raise and a commendation. Bob gets a warning to improve performance. Charlie gets to clean out his workspace and file unemployment.
Nah, in the real world Bob and Charlie will boast about how they got it done, and Alice was raised to be nice so she doesn't interfere. She's end up with the same salary but doing most of Bobs and Charlies work. Since Charlie was the most useless, he'll be the one getting the promotion in the end.
Yes, with a little more math it comes out that Alice is 7 times more productive than Charlie & in the project with all three, Alice did 54.8% of the work, Bob did 38.5% of the work, and Charlie only did 7.7% of the work.
In one hour Alice+Bob complete half the job, Alice+Charlie complete third of the job, Bob+Charlie complete one forth of the job. Adding all that we get that in 2 hours (since each name appears twice) three of them working together complete (1/2+1/3+1/4)th of the job. 1/2+1/3+1/4 = 13/12. Set up a simple proportion: 2 hours corresponds to 13/12 job, x hours corresponds to 1 job, so x=2/(13/12)=24/13.
4.5 hours is entirely believable - I've worked with people on teams who actually slow the whole team down - also, the Mythical Manhour explains how adding more people to a problem can actually make it take longer
Yeah, anybody that has worked anywhere would not have questioned that conclusion. It would have been more like, oh wow the math is actually accurate to real life for once.
I too see this every day. This question does not define the type of work. 4.5 hrs could be correct depending on the type of work. Since we don't know for sure, the answer should be impossible to determine without more information.
Seriously! Case in point: I drive a truck on a route servicing offices. Sometimes gal A goes with me to make things go faster. She has a lot of experience. Gal B works in the office and writes down the order in which I should service the stops. Gal B does not drive and has never ridden along in a truck to help out. Recently, I hit a stumble in the route and needed advice as to how to proceed given time and miles traveled. I called gal A to get advice. Gal A gave me advice based upon her experience. It worked out. But when I got back to the office, I was reprimanded for not having asked gal B. "Why would I ask gal B if she would have to go and ask gal A, when I could just ask gal A myself?" And, why should I burn up ten minutes trying to save ten minutes? It was reaffirmed by management that I must ask the lesser qualified and informed gal because that is her job. My take-away: "You expect me to be efficient, except when you expect me to be inefficient for arbitrary reasons."
OK. Well I'm looking at this purely from an 'efficiency' perspective (probably comes from my time as a manager for a call center). Firstly, if they're doing the same job at a constant rate, then Charlie needs additional training or performance management, especially based on Alice's and Bob's performance together. Secondly, why has Bob become less efficient while working with Charlie? Thirdly, I will give Alice the benefit of the doubt that she's highly efficient and that Charlie caused their time together to blow out by one hour, especially as Bob's efficiency seems to have declined while working with Charlie as well. So the common denominator of inefficiency seems to be Charlie. "Charlie, it's time to shape up or ship out".
So my answer is 2.55 hours. People will ask, "if the quickest time is 2 hours with two people, then surely with three people it has to be quicker than 2 hours"? Not so, taking the average of 'efficiency' over the three job tasks, this brings us to an efficiency rate of 72.22% or an inefficiency rate of 27.78%. Therefore with Alice, Bob and Charlie all doing the same job task together = 2 hours + 27.78% = 2.55 hours.
Easy solution: since, X =>2hrs for 1 work, ∴ x = 1/2 work per hr so we can just reciprocate... A+B=1/2 --① A+C =1/3 --② B+C =1/4 --③ since, eq1+eq2+eq3 = 2(A+B+C) (A+B)+(A+C)+(B+C)=1/2+1/3+1/4 2(A+B+C)=1/2+1/3+1/4 A+B+C=(1/2+1/3+1/4)*2 A+B+C=(13/12)*2 ∴Work per hr=13/24 thus, work = 24/13 now in terms of hrs & mins; 24hr 4min (approx 4 min)
“More people working on a job should get it done quicker” The reason most college students get this question incorrect is because they understand that... No.
But that is how that works, if they are for example building/painting a wall. Everybody works on their own part of it without interfering with each other.
@@nesnasimgoogle4580 - in quite a few types of jobs, adding people increases the friction, slowing down everyone. For example, if there are only two paint cans, now Charlie must interrupt Alice and Bob to get paint. Or, at the beginning, extra time is spent to find a new can for Charlie and to fill it for him. Which, in the real world, unless you have excess amounts of paint, someone will run out of paint during the job and will need to interrupt the other two for more paint. The real world is messy; algebraic problems are simplified views of the world where these non-numeric factors are ignored.
see, when the 3 people have to build a house they take less time because one starts with the wall, the other builds the roof and the third installs window and doors. and this makes sense because it is mathematically correct 😌
@@violinyay6632 - What you described cannot all happen at once, because the guy building the wall needs to build it BEFORE the roof or the doors and windows can begin to be installed. Math IS great, but it needs to be applied carefully, taking into account the knowledge of the real world.
@@billb7636 Damn, I forgot that gravity exists again. How does that keep happening? It's really embarassing. You should see me trying to build with Legos
Three days. See, Bob has a crush on Alice, but Alice is hooking up with Charlie, which accounts for the extra hour it takes the two of them together and the extra two hours Bob and Charlie spend arguing. If you put all three on the same task, the dynamic totally breaks down, Bob and Charlie both end up in 48 hour lockup and Alice quits because of the 'toxic work environment'.
Classic! That is so funny I work with a painting crew and I tell you it is exactly as you explained. I'm the foreman and I get so frustrated because I'll put 2 guys on a job that should take a half an hour and they are still in there 3 hours later! LOL LOL
@@smurfdurf5625 by your logic, I can tell you that it can take longer, because it also depends on who you are working with. Could be someone who distracts you, and could be a person who will help you
I went about this in a slightly different way. I thought, okay, if we assume the job is the same, then the workload is N, we're dividing that workload by the productivity of the workers, we get: N/(A+B) = 2 N/(A+C) = 3 N/(B+C) = 4 From there, I solved the simultaneous equations to get B = 5C and A = 7C, and thus, substituting the variables: N/(6C) = 4 N = 24C and: A+B+C = 7C+5C+C = 13C And so, 24C/13C = 24/13 = 1.846...
I read a comment saying that Charlie was a kid helping their parents in the kitchen, which would make perfect sense if you think about it. Edit: Actually nvm it doesn't make sense since it says 'job' not task or whatever.
My first thought when I saw this was that this is a very easy problem to solve. Charlie is holding back the other 2 employees. We need to find another task, if possible, for Charlie to do to see if he can do better at that task. But then I realized that Charlie’s feeling will be hurt if we do that so I guess the company is just going to have to add time to the assigned task so that his efficiency reaches the 100% mark.
Say there were 100 people working on the project. That 10 minute early completion time now means 1000 minutes of man hours saved (assuming everyone needed to be working for the full duration), so there are some cases where it could be beneficial!
If I had to guess, I would say he's the owner's nephew who just graduated High School and needs to pay rent to his Dad. Just don't tell any of the other employees.
I figured it out by seeing how much each could do in 12 hours. Alice and Bob can do 6 jobs in 12 hours. Alice and Charlie can do 4 jobs in 12 hours. Bob and Charlie can do 3 jobs in 12 hours. That equals 13 jobs in 12 hours, but everybody was counted twice so its 6.5 jobs in 12 hours or 12/6.5 hours per job = 1 11/13 hour per job.
Calling the problem "basic" is an overstatement. The problem itself is tricky unless you take context into consideration, but schools do not teach this, especially in math. Students learn systems of equations, but are taught to solve problems like this as simple equations rather than worry about percentages. I think the main issue isn't that college students can't solve this "basic" problem, but rather schools don't prepare students to solve problems like this correctly. In math, most students don't think about the context of the problem itself, but rather patterns in the problem and using equations and formulas to solve it.
Sry If your school was like you said. I learned in school to think before calculate, what could be a solution, and after calculation, can this solution be right.
Ok.. I plugged this into Wolfram Alpha: Alice is 7/24, Bob is 5/24 and Charlie is 1/24. Charlie should save 10 minutes off the job (1/12 of 60). It’s almost like an “are you smarter than a 5th grader question”. But I do agree though, schools teach too much by rote.
Not idea where u studied, but at my highschool I have done many problems like this in classroom lmao. it actually surprise me that college students are having problems with this kind of basic equation.
Well, Alice and Bob have good chemistry together, so they get the job done fast. Alice and Charlie don't mind each other. Bob and Charlie actively dislike each other, so when they all group up to get the job done, Bob says: "Charlie, no offense, but me and Alice alone would get this done faster than if you weren't here, so go do something else." 2 hours.
This is exactly how it goes in the real world. Except the beating. It's a lot more fun to watch Charlie struggle for 5 minutes trying to tie his shoes, only to finally manage it and realize he put them on the wrong feet.
Nah actually Alice and Bob wanted to finish the work so they send away Charlie to get a coffee and the guy disappeared for almost 2hours, they finished early because they where thinking of finding him to see what he was doing, they just didnt do it before because they wanted to at least finish the job
Intuitively, the best way to understand it is by calculating how many times each combination can complete the task in a 12 hour period (12 is a common multiple of 2,3,4) A+B=6 A+C=4 B+C=3 therefore A=3.5 B=2.5 C=0.5 and A+B+C=6.5 so we convert it back into our 12 hour period: 12/6.5 = 1.846... = 1h50m46s
So you want to promote the worker who is best at the current job and slow down your production. Why not promote Charlie he might be a fantastic manager
You're wrong about Charlie. It took him only 9 minutes to do the job and get it right. It took Bob 2 hours hours but left everything screwed up. Alice didn't do sh!t. Nympho Alice distracted Charlie so it took him 2 hrs and 51 min of fighting off Alice. Charlie had to spend 3hrs and 51 minutes correcting Bobs mistakes. Charlie was able to complete the job correctly in 9 minutes but it took 1hr and 42 minutes trying to get Bob and Alice out of the closet.
I never heard of ISTJ before, I read about it and it sounded like me (which I expected after this comment). So I took an online test and it told me I'm an INTJ, I wasn't sure which one fits more to me so I did another online test and again ended up as an INTJ. But I still think that depending on the situation I'm something in-between.
Yeah, based on those numbers, Alice can do the job alone in 3.5 hours (which is less than the other two together), Bob can do it in about 5, and Charlie left to his own devices would need 24 HOURS!!! Let the woman do her thing!
I had a simple answer: Charlie slows people down, so he needs to sit back and let Bob and Alice get it done the fastest, in 2 hours. We also just have to keep Bob focused because according to his work with Charlie, he gets distracted easily and takes the longest in the combo
Charlie doesn't slow things down he just works more slowly but is still making progress, not slowing it. Letting Bob and Alice do it alone is 9 minutes SLOWER than if Charlie helped.
As somebody who used to work in retail management, this is the correct answer. Charlie should be assigned to a different task that will allow him to work at his own pace or one that doesn't have to be perfect, but is repetitive, and he can rush through to get it done.
Charlie had special needs and discrimination will not be tolerated. Now Alice and Bob both lost their jobs because Charlie viewed Alice and Bob's comments about "working too slow" as harassment. Now the whole operation is run by Charlie. Moments later, everything has been outsourced to a disadvantaged country to avoid bankruptcy. Everyone loses their jobs, and Charlie is the only one qualified to receive social assistance because he has special needs.
An improved explanation of my (earlier) 'equivalence & comparative efficiency' solution: The average 'completed task' contribution = 4 hrs. apiece for A & B (2 hrs. combined) / 6 hrs. apiece for A & C (3hrs. combined) / 8 hrs. apiece for B & C (4hrs. combined). C'quently & importantly, A B & C can be dealt with as 3 individuals who are simultaneously completing a task that - separately - would take 4 6 & 8 hrs. respectively. Based on A: B's efficiency = 4 × 4/6 = 8/3 & C' s efficiency = 4 × 4/8 = 2 such that - working simultaneously - A B & C would take 4 ÷ (4 + 8/3 + 2) times as long as 4 hrs., in completing the task. Specifically: 4 ÷ (12/3 + 8/3 + 6/3) = 4 ÷ (26/3) = 4 × (3/26) = 12/26 -- i.e. -- would take 12/26 of 4 hrs. = 48/26 = 24/13 hours. (Working in combination @ their individual efficiency rates.) Rgrds. - R.G.S.
Charlie sent me an email from Goa, asking me to wire him some money for a plane ticket home. I bought him the ticket instead. I don't trust him enough.
@finger speak if we were resolving this problem with physics methods WE would take in count one more parameter to describe this "group is slowing down individual values" thing
My daughter, when she was at UGA, found it saved time when assigned a group project, to just say she would do the entire project herself. That was after a group she was in was unable find time to meet together to finalize a report, so she had to complete everyone in the group’s assignment the day before it was due. The person who commented that Alice could have done it faster if the guys would just get out of the way was right.
I detested group projects. One professor had us anonymously submit grades and evaluations of the other group members. My group was three women and a VGL guy who always made sure we knew he was going to be late for a date because of our meetings. I was the only one who submitted an honest evaluation. The professor gave the women As and Casanova a B. Everyone was shocked and wondered why. 😈
My daughter was a straight A student and she hated it when teachers assigned assignments to be done in a group because other students never did any work they just fooled around and she ended doing the whole thing to just get it done. She always carried the load and the others took advantage of the situation and got a better grade thanks to her efforts. Most students have a very poor work ethic and never get down to business to complete anything.
@@patsmith5947 But this is exactly how the real world works. The reward for doing your job well is always getting to do somebody else's job and if you don't know who's job you're doing....somebody is doing yours.
I'm guessing Charlie is the son of the owner and gets promoted to manager, Bob gets promoted to supervisor and tries to employ as many Alices as he can find to get the job done.
I just made the job concrete. They had to move 24 boxes. This showed me that Alice moves 7 boxes per hour, Bob 5, and Charlie a measly 1. So in total they can move 13. Then it was just dividing 24 boxes by the 13 per hour.
If they are conjoined nonuplet sisters ... maybe? But Csection would be difficult and birthing canal obviously impossible. Unless it was human centipede set up and not some giant fleshy leg ball. Also assume genetics didn't prefer twins or greater which obviously would decrease the effectiveness of this freakish uber-womb, and break all known laws of reality TV baby shows. Causing mass hysteria, looting, etc! And of course , to top it all off. It's just crazy to think 9 bitchy pregnant woman could stay that close to each other for even a month without some poor sap walking by and finding out just how much they hate men, or anyone trying to touch their babybump. Dead . Dead by nonuplet stabbing. ... No this would not work. Also, I've decided that I may have given this too much thought.
n dang it .... the creature cant take much more math changes , before she/they mutate, and things really get out of hand. I figured confidence would carry success forward. Not any more, thanks! Lol. Jk The visual haunted me for a couple days after I posted. Btw. It's some SCP stuff for sure.
Alice and Bob should lock Charlie in another room and they would probably do the job in under 2 hours because they did it before in 2 hours, that means they know what to expect and do it a little quicker. So I came up with 1 hour 52minutes. 1 minute longer than your solution because they had to shut Charlie up from banging on the door.
Yeah, but you KNOW Bob and Alice are going to start getting it on, I mean Alice is sooo easy. The next thing you know the whole afternoon is shot and Charlie gets blamed because he's the slow one. Alice will get promoted and Bob will be overcome with guilt for his decision to sleep with Alice and confess to his wife. His wife will make his life a living nightmare until the marriage ends in divorce and he finally spirals into a well of depression and drinking and ultimately the loss of his job. Alice will fire Charlie and replace him with a minority who can easily get the job done alone in 20 minutes but has no real incentive to do so due to low pay and discrimination. In the end, the new hire slips on his way into the building and sues the company into bankruptcy. So Alice, Bob and Charlie can get the job done in infinite time...final answer.
@@ProfessorOzone Definitely not the final answer. When Bob and Alice get married, they will have 2 children who will grow up and do the work for them. Ha! Ha!
@@chrisweyers4764 Oh Dear! We've just created another problem. I wonder what country they are in Mmm! maybe America, in which case problem solved. They could be called Bob I or Bob Junior and the same for Alice, wait a minute, I have never heard women with the extended title before, except for British royalty. Oh Dear! the problem gets deeper.
The "work done per unit of time" is the inverse of the time used to complete the work, so it is possible to just simply solve: a + b = 1/2 a + c = 1/3 b + c = 1/4 summing up all three equations: 2a + 2b + 2c = 13/12 --> a + b + c = 13/24. The solution is the inverse of it, that is 24/13.
Also thought of this in terms of rates, starting with making 120 widgets, A+B make 60/hr, A+C 40/hr and B+C 30 Hr. Adding the first 2 together 2A+B+C=100, we know B+C=30 so that means 2A = 70, or A=35 per hour simple maths from then on gives B at 25 per hour and C at 5 per hour or 65 per hour aggregate. 120/65 = 1.84 hrs (1hr 50min 46.15 sec approx.)
Yes, it is easier to assign variables to the entire individual rates, not just the individual hours. Excellent, Michele! I used Substitution while keeping everything as a fraction leaving out a discussion of percentages, which can be confusing for many students. This also was a much quicker process. I hope you teach Math or Physics or something because your students would be blessed to have you as their instructor.
I don't know how but I almost got this answer by doing the common mistake version but using reciprocals but then I flip the reciprocal and got the wrong answer. I don't know how this happened.
"Now, before I solve this, let me talk about a common mistake. Many people see the first line and translate it to A+B = 2." -> Sad me looking down on my paper. First line: A+B=2
Even before doing any math, I can safely say Charlie should probably be fired. Bob is probably an average worker, and Alice should probably be promoted or given a raise.
@@rodicow3491 That is the way the real world works, the real worker gets all the S@h@t rolled down on himself while the others get praswd and paid more to do less work.
I have experienced this directly when running a landscaping crew in my twenties, myself and my co-crew lead could get a yard done faster alone than with a crew of four. We would have to delay and wait for the others to finish their tasks before we could proceed with ours. After a week we tried dividing the teams, dropping one of us off with one of the others at one yard and then whoever was driving that day would take the other crew member and do another yard, this took even longer, week 3 we dropped the other two off and went and did on average two yards before they would finish one, at the end of week three we fired the other two and gave our selves a raise with the savings from their wages.
Way to make a problem way more complicated than it needed to be. Convert from times to rates: A+B=1/2; A+C=1/3; B+C=1/4 [all in jobs per hours] Add up both sides of all three: 2(A+B+C)=13/12 Simplify: A+B+C=13/24 Convert back to time: 24/13 [back to being hours]
Yep, much simpler. The maths is technically identical, but much easier to understand each of the subsequent steps after you make the initial conversion.
Yes, jobs-per-hour is the key concept, gives 3 equations for 3 unknowns, better to solve them as such, rather than looking for a trick, in this case adding all 3 equations, which works in this example, but might not work in other examples.
@@climanrecon5649 well adding all 3 equations is just a shortcut to forming a quantity proportional to A+B+C. In either method it could be done by individually solving for A, B, and C, but that's more work than is necessary
@@thomasr5302 Assuming constant rates is a good clue, but it leaves out a critical assumption: that there are no interactions (in the statistical sense). In other words, we must also assume that each person works at the same rate regardless of who else is working with them. As a real-world counter-example, my guess is that it would take the three of them about 24/7 hours to do the job as a trio, because Alice would end up doing everything while Bob and Charlie worthlessly compete for her attention.
6 hours. Seeing how the time takes longer with Charlie working, and less with Alice, its obvious Alice is grounded and Charlie screws around. Bob is gonna get pulled into Charlie screw around and Alice will take longer trying to get the other two to work
Sadly this is a very common occurrence in fast food jobs. You'll always have a couple hard workers and a BUNCH of lazy bums that make the good workers seem bad too. Its harsh to work your ass off and then get told by customers that you're paid too much.
Charlie's work of 1hr51min = 111 min. Alice will get that job done 7 times faster = 111/7 = 15 minutes. Bob will do that 5 times faster = 111/5 = 22 minutes. Alice and Bob dividing that job will do it 7 + 5 = 13 times faster = 111/13 = 8.5 minutes
My teacher taught this to me when I was 12, shame I lost track of it... Guess I got to brush back up. I only knew that it'd be quicker, but not by how much...
My silly way of thinking about it: If A & B can do it in 2 hours, then they can do it 6 times in 12 hours. If A & C can do it in 3 hours, then they can do it 4 times in 12 hours. If B & C can do it in 4 hours, then they can do it 3 times in 12 hours. So A & B & A & C & B & C together will do it 6+4+3=13 times in 12 hours. That's two of each person, so one of each will take double the time:13 times in 24 hours. If it takes them 24 hours to do it 13 times, then it takes them 24/13 hours to do it 1 time.
What do you mean by "thats two of each person, so one of each will take double the time", do you mean that because since its pairing, you times the fraction by 2 because you divide the pairing to make it 1 person?
@@luminesent I mean that 2A, 2B, and 2C, will finish the task in half the time as A, B, and C will. Exactly double the people means half the time taken.
Not silly at all. This is a "verbal reasoning" representation of what Presh says with mathematical equations. It may well be a better representation for many people.
This approach makes it easier for me to understand. Finding the common denominator first is making the whole thing easier to conceptualize. Before I watched the explanation I was trying to solve the problem with averages, but I ended up with an answer of one hour. I knew I was doing it wrong. You should teach math if you don't already.
Being a contractor, I came up with about 11/2 hrs. unless it’s a union job then I figure it will take a week counting lunch breaks and coffee breaks with phone calls and bathroom breaks thrown in . Good luck 👍
Up yours Ron, if employers would have treated their workers fairly from the start unions wouldn't have been necessary. If your union workers have that many perks then it is your own fault for not being smart enough at the negotiation table. GO Union strong. Teamsters 0471.
@@chezman3892 - when I was in a union, it was the PBA , money for nothing as far as our dues, like today all they did was role over and play dead whenever our contracts came up. If you’re in a good union more power to ya mine pretty much sucked.
Alice will do most of the work, Bob will help somewhat but mostly get in the way, Charlie will spend the two hours taking credit and brown-nosing the boss and will get promoted before Alice or Bob. Then he'll continue to give them all the work.
Alice and Dilbert (Bob) work together while Wally (Charlie) drinks coffee and reads the newspaper in his "office." After much labor the PHB informs Alice and Dilbert the project was cancelled a couple of months ago due to a reorganization. So Wally turns out to be the only winner here...as usual. So C>(A+B) and PHB
@@pragalpaah4314 Of course!. If Alice is alone, she doesn't get distracted. If she works with any of them, she does. Don't you see the problem? Is called hormones.
I solved this by effectively using the parallel resistance formula: 1/A + 1/B + 1/C = 1/t, solve for t. I came up with this by realising that, instead of adding the times, I should be adding the speeds. And since speed = distance/time, I set distance to 1 and added. Then, since time = distance/speed, I did 1 over the total and got 24/13. You can use any positive number in place of 1 and it still works.
Charlie? Bob's the slacker. On second thoughts, maybe Bob fancies Alice, and not Charlie, so when he works with Alice he's trying to impress. Whereas when he works with Charlie, he's trying to get him fired so he can work more with Alice.
@@myrmaad or any government. My wife works in care in the community and her current director of service has failed and been moved around for the best part of 5 years. The manager is still crap, but higher paid crap. She works for a local metropolitan council in the UK.
Great video! However, regarding "Does this answer make sense?" As an engineer, I promise that it is entirely possible that adding "helpers" can increase the amount of time it takes to complete a project, especially when it's done late in the game in an effort to correct a slipping schedule.
Yep. That has been my experience in SAP Functional for projects when management assumes throwing people at it will reduce the time at the same rate. The same logic that killed 60k British soldiers at the Battle of the Somme during the first day. Real life is never the same as theory, and people need to respect the realities of human nature and the limitations of scare resources with alternative uses.
The first answer makes perfect sense if you are contractor. - "How long time will it take?" - "It will take two hours for me to do it. If you want to help, it will take four and a half hours."
The solution is to let Alice do the work alone. If Bob is getting in her way, it takes her 2 hours to overcome his antics. If Charlie is getting in her way, it takes 3 hours for her to fix his half baked semi-effort. So it's a bloody miracle that when Bob and Charlie toss the towel into the ring and call it quits after 4 hours that anyone would consider that work being done. Alice could probably sort the thing out in 30 minutes or so, it's just those blokes getting in her way that mess things up.
Alice alone would take about 3 hours, 25 minutes, and 43 seconds to do the work. Alice does 7/24ths of the work per hour. T(Alice)=24/7 hours to be exact
@@shkhrvarshney precisely. Alice does the job in 30 minutes by herself. Since we were never given an individual initial condition of how the people work when they work alone we don't know whether Bob adds time to the job. He might have different requirements for what needs to get done or simply complete his portion of the job that much slower. Alice does her work in 30 minutes and stops because she has other things to do. Then Bob works for another hour and a half to fill out his timecard.
@@shkhrvarshney that way regardless of who they work with Alice consistently completes the job in 30 minutes, Bob takes an hour and a half, and Charlie takes two and a half hours.
The answer is simple, workers Bob and Charlie are fired, Alice now has three times the workload and quits. Infinite time required for all three as none are working there any more.
No, fire Charlie, give Alice the raise she deserves, hire an intern to replace Charlie and have Alice train them,, and tell Bob if he doesn't pick up the pace, he's not getting his production bonus
@@kenworthcowboy9739 In the "real" world, Bob and Charlie are fired, Alice is given the additional workload but no increase in pay. Then, she quits. Been there - done that.
Nah, open a plant overseas where you do not care if it takes 10 hours for 6 of them to do the job because labor is so cheap. Promote Alice to go overseas and train the employee at the new plant on a 6 month agreement but do not renew her term.
I did not figure this out. I am a 58 year old man with minimal education who failed high school math. But I realized almost immediately that the answer must be a little less than 2 and then I got hung up on whether the answer should be expressed as a fraction, or as a decimal.
@@user-unknown173 probably due to the law of diminishing returns which states that if a varying factor (in this case the number of people working) is increased to a fixed factor (the room they work in or something) the returns (the hours they take) will decrease (increase in this case) as the variable goes too far. This is not a math thing its actually a business thing. Thing like what happens when a balloon (the fixed factor) is blown (the varying factor) too much.
Alice is so smart that she makes the manager feel threatened. She takes on so much work and expects compensation but they decide not to give it to her because then it would affirm that she is too good for the job and management. So they keep her wage low until she gets upset and leaves. Leaving Bob and Charlie with too much work and a failing company. Should have just paid Alice what she was worth because now everyone loses.
Yes indeed. Alternatively, they tell Alice "Sorry, we don't have the budget to give you a raise. You need to be a team player and suck it up for the good of the company. By the way, here's some more work." Alice quits and the company then hires three people to do her job.
@@GayleHallAZ *situation or state, not "the reality." The vile phrase "the reality in X" is a generic mouth-breather misuse of the word "reality." Misusing as if it means "a given or personal situation." Reality is not a plaything, there is only one and it is absolute; we play within it. We can never compartmentalize~control anything but our opinion regarding reality. Means there is no such thing as "realities" for that makes them all falsehood~belief and not actual reality; *the singular~universal substrate of all other things*
Alternative way:- We know, Efficiency( rate at which work is done by one) and time are inversely proportional to each other.[ i.e. The more someone takes time to finish a job, the less efficient he/she is and the less someone takes time, the more efficient he/she is.] Time taken by Alice(A) and Bob(B) to complete the job= 2 hours Time taken by Alice(A) and Charlie(C) to complete the job= 3 hours Time taken by Bob(B) and Charlie(C) to complete the job= 4 hours Work done by A and B in 1 hour= 1/2 Work done by A and C in 1 hour= 1/3 Work done by B and C in 1 hour= 1/4 Work done by 2(A+ B + C) in 1 hour= 1/2 + 1/3+ 1/4 =13/12 Work done by (A+ B + C) in 1 hour= 13/12* 1/2 = 13/24 Hence, time taken by Alice, Bob and Charlie to complete the job is (24/13) hours.
4.5 is now pronounced "four fifths" (2:19).
..so .11 is pronounced "zero elevenths"?
Rofl, gold. The true riddle is solved.
CQUNC I noticed that too. xD
9/2 = 4/5 good to know
#FakeMath
I work in software development, and everyone in that field knows that the more programmers you assign to a task, the longer it will take.
was looking for this comment
You don't even need to be a software developer to understand. Chefs working with limited kitchen space is a good enough example of this. The most important thing is that there needs to be an adequate amount of work for each person to work efficiently. Software development has plenty logistical implications that come from bigger teams.
First Surname its a joke
Funnily (or not) enough, it's based (and reinforces) a belief that can have a negative impact on planning...
+Nathan How so? I think people understand when a larger team is needed for a task, and when a task can be done by a smaller team. It's mainly just common sense. Having too many people on a simple task just wastes man hours (which are expensive). Conversely, having too few people on a big task however risks you not meeting deadlines.
Again to use food as an example. A waiter knows what it's like to both be over-staffed and under-staffed.
This saying is not a religious belief. The saying arose because of observations.
The real answer is: "Charlie you only saved us 9 minutes. You're fired.”
316ht under rated comment
Agreed
it took bob and charlie 4 hours to do the job that alice and bob did in 2. charlie needs to get fired
Exactly. Well put 316ht.
Hahaha this is gold
I know this is a math problem and all, but everything I've seen in many different jobs tells me that Bob and Charlie should get out of the way so Alice can fix everything, so they can all go home.
LOL
So true...
Charlie discarded only 9 minutes of Alice's and bobs work, what a useless person
Bob and Charlie are distracted by Alice's feminine attributes! 😜
Especially Charlie. Poor sod can't think straight it seems...
Definitely
i'm more astonished by the fact that charlie makes the job only NINE MINUTES shorter, than by the actual solution itself
In 1 hour he does 1/7th as much work as Alice.
Charlie must be part of management.
ikr 😂
I took a detour and I think I found out it takes Charlie 24 hours to complete the task on his own. I think it takes Alice 3.42 hours on her own.
@@TheLastSoundNL Even Bob by comparison does the job in 4 hours and 40 minutes just by himself.
"When 3 people work together they should take less time than 2 people."
I feel charmed by your naivity.
Three people is a Union, and the job never gets done.
The work effort each put out is a constant
Paul Googol the key word is should
@@hermanstanford4388 a constant struggle
@@hermanstanford4388 You can work at a constant rate and still end up worse off than when you started.
charlie is that guy that writes his name on the project but was never there doing it
It's more Bob
What if Charlie upped the quality significantly at a deeper level of analysis, while the cooperation among the three allowed it to be completed at 9 minutes less? yeet
My thinking "Bob is irrelevant, Charlie sucks, the time will be equal to the amount of time it takes for Alice and Charlie, so 3 hours." While I was technically wrong, I feel my answer falls within the spectrum of likely real world outcomes.
Charlie does work too! He would finish the job alone in 24 hours.
Bob is worth 5 Charlie’s
Alice is worth 7
Charlie was fired that same day
That means the answer is 2 hours XD
Answer is 0. They’ve already done the job 3 times.
Obviously they all did it wrong if they have to do it again. I wouldn't trust them to get it done in their combined times let alone 1hr51min.
It's shoveling snow
Lol
Lol
SupremeHorizon not necessarily. They could be vaccuming the house and they do it each week.
Also, Alice takes about 3h26 to do a solo job, Bob takes 4h48, and Charlie takes a whopping 24h.
The conclusion : fire Charlie and hire someone else.
u calculated for each person?
The conclusion: Charlie is the manager and Alice is working a summer job until she finishes college. Bob is Bob.
@@BigMac4459 Bob is Bob
I'm surprised that Bob would agree to work with Charlie again, seeing as he has to spend twice as long at work if he is paired with Charlie, compared with when he is paired with Alice.
@@kwilson5832no choice- charlie makes the schedules
Real life answer is two hours. Alice and bob do the task while dipsh$t just watches
Lol.
i though the same thing. or what if bob did no work. the the answer is 3.
Just depends on who was the "supervisor"
it would take charlie 24 hours to get the job done (ignore my name)
you sir are about to put all the charlies on tilt
“More people working on a project should get it done quicker.”
Oh, honey.
Depends how many of those are managers
FOR REAL
Charlie seems like dead weight, he just sits back while Alice and Bob do it in 2. solved easy
Problem kind of ignores diminishing returns. Picture three people working in a 5X8 foot bathroom, one painting, another installing a new supply and faucet to the sink, and the third putting in a shower surround. Total job will get done faster if they work on their individual part at different times.
Also, yeah, Charlie should be fired, and from the look of the times Alice might deserve a raise.
That was my thought too, realistically it probably took the 2.5 hours with all of them working on it.
The answer is that Charlie will be unemployed VERY soon.
Naihonn. Agreed... So the answer will become 2 hours. 😎
Naihonn I think Charlie must have shown up to work in a full body cast.
Naihonn I have lived a few years and my experience is the less capable you are. The better job you get. Stop trying so hard. Life is easier than you think.
What a life moto. Stick to being incapable kids!
Charlie works at a Union wage and at a Union pace.
I thought about it a little differently than the 'percentage' system. I thought of them as rates. Alice works at 'a' jobs per hour, Bob at 'b' jobs per hour, Charlie at 'c' jobs per hour. Adding their rates together, Alice and Bob would work at the rate of 1 job per 2 hours, so the equation is A + B = 1/2, with the units being 1 job / 2 hours. So you'd get:
A + B = 1/2
A + C = 1/3
B + C = 1/4
Using the neat little trick and adding all of them together, you get
2A + 2B + 2C = 1/2 + 1/3 + 1/4
2(A + B + C) = 6/12 + 4/12 + 3/12
A + B + C = 13/24
All of them together can work at the rate of 13 jobs per 24 hours, and if you want to know how long it takes them to complete 1 job, just invert the answer: 24/13 ≈ 1.85 hrs. Charlie needs to step his game up.
This is the way I did it. You quickly see that you have to deal with rates due to all working simultaneously. The wrong answer of 4.5 is actually correct if A, B, and C have to work sequentially and not in parallel.
I used this method too! And it's crazy how many people got it wrong, since I was taught this in 8th grade
That's how I solved it too, in my head in 15 seconds. 😊
That’s basically how I figured it out, too
@@micknamens8659took me longer than 15 seconds, lol
"It takes less time than any pair working together."
Sounds like you have never been involved in a group project in college.
Do they work at a constant rate?
@@carrymesenpai3276 no
@@jacobmontemayor6685 obviously, which makes this comment kind of obsolete, an out of context joke at best
In college? in the real world.....the more people involved, generally, the longer it takes.
@@muskokamike127 yes but that was never subject of the discussion
my brain immediately went “well alice and bob are still part of the group so it’s still 2 hours because they would just ignore charlie since he’d be slowing them down”
Judging just by what the problem reads, Bob is either the slowest worker or he tells a lot of really good jokes.
That was my conclusion as well
I concur dr
You’re right because it takes 9 minutes faster with Charlie because he helps for the first 5 minutes then sits in the corner.
That was my thought too. I thought it was a trick question like "if a rooster lays an egg on a roof, which direction does it roll?".
Two hours. You sideline Charlie, since he's clearly sandbagging whoever he works with.
Same lol, I also thought it was two hours. Turns out it is less than that.
@@nandantandel1604 Technically you're right, since if you round off 1 hour and 51 minutes then you get 2 hours
So if this problem was in a real world situation charlie absolutely didnt do anything
If he only saves 9 minutes of time, he's not worth employing anyway.
@@peppermint1050 Spoken like an engineer
I have 20 years working as an engineer. After i solve any problem, I always apply a common sense check. This is something i see most beginning engineers skip and it causes them to not catch most of their errors until the errors have culminated into an obvious failure.
It's one of the most powerful aspects of math, that there is OFTEN PLENTY of common-sense checking of things, to help reduce human error significantly.
The fact that massive amounts of college students now apparently have NO CLUE about this says it ALL, re the state of the modern education system (in the US, anyway), IMO.
"A common mistake is that students turn the names into variables and turn the sentences into equations..."
* quietly crumples paper before shoving it into my mouth *
I made that mistake...then I made another mistake. I finally settled on a third mistake.
I hate to admit that I was so sure about myself that I almost didn't click on the video to check the answer.
@@Armando2609 I feel ur pain man, 4.5 gang where u at 😎💯💯
Well I'm not a man :P
@@Armando2609 its an expression not a statement bro 😎👍
"When 3 people work together, it should take less time than when only two people work together." You've clearly never worked with a "Charlie" 🤦♂️
Group projects always take longer. Murphy's Law demands it.
Yup - in my experience if you have 2 people wo are really good at their job (like Bob and Alice clearly are) and you add a third worker who is a dog... the first answer is probably more accurate.
"Too many cooks spoil the broth." Its a proverb for a reason.
Haha sooo true!!!
@@Fickji nope.
Actual Answer: 2 hours. Alice and Bob tell Charlie to sit this one out since he tends to slow them down.
Charlies average is actually closer to Alice's according to the information given. I came up with 4 hours with all 3 of them working to gather. I dont disagree with the fact that working with Charlie wouldnt be the most efficient.
charlie calls them both racist and spends 6 hours in the h/r dept attempting to get the other two fired alice spends 5 hours in h/r with a claim of sexual harassment on both bob and charlie says she wants a raise and promotion and bob spends 5 min dropping off a i quit notice at h/r because he is sick of working with either of them lol
That is the logical conclusion . Charlie can stop others from interrupting the work or "trying to help" . .My first thought was Alice can do it in an hour by herself .
Absolutely.
I was thinking the same thing.
I have been in management for over 25 years. This is what I can see from this problem in the real world.
1: Bob and Charlie are friends. This explains why the task takes longer when it is only the 2 of them.
2: Bob is the harder worker between Bob and Charlie. It takes longer for Charlie and Alice to complete the task.
3: Neither Bob nor Charlie likes working with Alice. Both Bob and Charlie take less time to complete the task when working with Alice than when they work together.
4: The "wrong" equation is most likely accurate in the given scenario. When all 3 are working together, Bob and Charlie will spend most of their time talking and goofing off. Poor Alice will have to do most of the work. Therefore, it will take longer, with 2 of the 3 not working and spending more time playing grab-ass with each other.
This.
The job will never be completed. Alice, Charlie and Bob have been working on this same job since I was in school. If they haven’t finished it by now, they never will.
🤣
You are awesome
can confirm we are still working on it
@@Bob-hh8rp 😂
Its cuz when charlie and Bob are together they just goof off and Alice cant do it by herself
The person who thought up this question has clearly never been in a college assignment group.
This a question for averge US teenagers
@@insomniac5129 They mean to joke in the "work is constant no matter how many people you put on the job" for this equation.
@@Xeneonic Well I didnt see that lol
Exactly. They probably never left their mothers womb somehow to be precise.
The real answer is 4.5 hours. Alice, Bob, and Charlie are good friends who enjoy each other's company, so when they are working on a task together, it takes longer.
Joe E. I came up with the reason for it taking longer was because they didn’t get along and kept nagging at each other and arguing... 😂
Or they made it to the best quality
"Assume each person works at a constant rate, whether working alone or working with others."
Harvard needs you
Must be friends with benefits then :)
This solution is easier for me:
Change hours per work into work per hour (wph for convenience) to get
A + B = 1/2
A + C = 1/3
B + C = 1/4
Now solve:
A - B = 4/12 - 3/12
A = B + 1/12
B + 1/12 + B = 1/2
2B = 5/12
B = 5/24
A = 5/24 + 1/12 = 7/24
C = 1/4 - B = 6/24 - 5/24 = 1/24
Now consider
7/24 + 5/24 + 1/24 = 13/24 wph
1/(13/24 wph) = 24/13 hpw
They are doing 1 work, so
(24/13 hpw) * (1work) = 24/13 hours
"To the professors' surprise, many of the students set up the wrong equations and could not solve this problem" -- This is a fairy tale. No professor would be surprised by that.
it should be : professors are happy, as they successfully setup those naive student who have too much confidence
Actually, the professor would count them all wrong. The professor would say the correct set up would be to let the government do the task while the 3 workers where on the draw from the government!!
@@vergilw7009 Or 'the professor busted the new students' arrogant & over confident bubble.' 🤔😅😉
At least they know all the 102 genders which is way more important :D
... nor would a professor be surprised that they turned in the resulting (wrong) answer. A more intersting question is: of those who turned in the wrong answer, how many knew it was wrong vs how many didn't even think about it. A follow up question is: of those who knew it was wrong, how many of them actually felt some kind of remorse (as opposed to those who were perfectly content to have something mathy-looking on paper.) Sorry, Mr. Talwalker, but in my experience, concern for the rectitude of one's math homework was non-existent among almost all of my peers -- even at the college level (and even at a highly respected science and engineering school, no less!) My contemporaries were masters at playing to the curve. They'd've seen this problem as a quickie free-bee and moved on as fast as possible.
Glad to know I wouldn't do the incorrect method.
Or the correct one for that matter
Yup
Hey at least its progress
Honestly I think most find the wrong answer and knew it was wrong, they just had no idea how to do it right. At least that was me. I only didn't bother to do equations
I got a really close answer using the incorrect method; I did the incorrect variable assignment but set up a final equation A x B x C instead of A + B + C and I got 1.875 hours or 1 hour 52 minutes 30 seconds. Really close
Yeah. I was on the right track but I had the "1" on the wrong side of the equation.
@@waelnawwal it depends on reasoning tho. The wrong method makes no sense at all, even if it cn be described using words. Dw im also a victim of this problem
The funny thing about questions like these is people always go: "It wouldn't make sense for more people to work on a task and have it take longer." My response is always, "Clearly you have never managed employees."
The problem does state that they work at the same rate regardless of who they work with.
Even ignoring the social psychology issues, most tasks are restricted physically or logistically in how many people can effectively work on them. 3 people can't wash dishes in a single sink, for example. The math problem assumes a very particular sort of task.
Yeah, math never takes decreasing marginal utility into account.
Alice stood around chatting and it still took four hours.
You are welcome.
I found the manager that sits on his/her ass all day and has no idea how to actually do the job or even tie their own shoes for that matter. Plugging in names on a schedule and entering fields on a payroll application is so hard, isnt it?
As a side result, we can notice that Alice's relative working efficiency is 7, Bob's 5 and Charlie's 1.
Yep!
"When more people work together it should take less time, not more time"
Sounds like you've never worked in Software development
Sounds like you stole the popular comment
Josef Aguilar
Or had a VP involved.
Oh, wait.
They mentioned work.
You can’t get 9 women pregnant to get a baby in a month
HappyCat3096 How would the 9 women work together tho?
@@HappyCat3096 Yes, you can, but the women have to exist in separate dimensions and then you need a wormhole to combine 9 babies into one.
Here’s my solution:
Bob and Charlie must be dating, so they’re the most distracted when they work together because they’re all lovey-dovey, which is why it takes them 4 hours to finish the job.
Alice and Charlie are close siblings, so they waste an hour or so talking while working together.
Alice and Bob don’t really know each other well, so they’re able to focus more and finish the job in 2 hours.
If all three of them were to work together, then Alice will realize that Charlie and Bob are dating, and she’ll start being very protective of Charlie because she doesn’t trust Bob with him (she’s an overprotective older sister and doesn’t know Bob very well). This will lead to an argument that results in bruised feelings, potentially damaged relationships, and no work done. So they never finish the job.
I’ll take my Nobel Prize now, thaaank you :D
Yup. Accurate!
After that Bob’s friends Daniel and Ethan come in and start fighting and now their relationship is broken which results in stress-working, and now the technical work/h is actually higher. They are now working separate jobs with efficiency. Now the work per hour is higher than Alice, who is sobbing in the corner.
This is dangerously accurate. O.o
@@anantmalik You know, I’m something of a scientist myself.
@@EMLtheViewer Good evening Mr. Emalan. I am almost a scientist. I am a Ph.D. A Doctor in the fields of Management and Psychology. Nice to meet you. :)
What this video taught me, more than anything, is you can use math to get the right answer and still have it be totally wrong in a real life scenario.
When ever you see "assume that" in a math or science problem you can assume that it will be different from a real life setting.
Depends on what real life scenario you're talking about. You're assuming these are people. We could be talking about 3 roombas.
@@misterkite - Dammit, now I want a Roomba so I can name it Alice The Overachiever.
🤣😂👏🏻👏🏻👏🏻👏🏻👏🏻😆
So funny but the wrong initial answer is probably the most accurate. When doing construction In a limited area, more people can just complicate things.
In india we are always taught to calculate using 1 hour's work i.e the work done in 1 hour which is in this case is 1/2, 1/3, 1/4 respectively. I did it this way and got the answer correctly.
Now seeing your video it makes sense why we used to take 1 hour's work instead of the actual time taken.
Thanks folk! 🙂
However you have to do the reciprocal of the answer obtained in order to get the time because it's just the part of work all three could do in an hour.
Charlie really is not contributing much, is he? Barely 9 minutes time save over two hours if he helps Alice and Bob
Alice is the real MVP here
How did you work out that charlie only did 9 minutes i don't get it
Alice+Bob= 2 hours
Alice +Bob+Charlie =1 hour 51 mins.
The time was decreased for 9 mins when Charlie worked with them..
@@waraulhasan2477 XD
Work rate per hour for the individual persons:
Alice: 7/24, so she would perform the task in 3 and a half hours.
Bob: 5/24, so he would perform the task in slightly less than 5 hours.
Charlie: 1/24, so he would perform the task in 24 hours.
Lay off Charlie he's a show learner and new to the job! But one he gets going..
So Alice deserves a raise and a commendation. Bob gets a warning to improve performance. Charlie gets to clean out his workspace and file unemployment.
Brian Weeks: Best comment! Thanks for a much-needed laugh! 😂😅🤣
Nah, in the real world Bob and Charlie will boast about how they got it done, and Alice was raised to be nice so she doesn't interfere. She's end up with the same salary but doing most of Bobs and Charlies work. Since Charlie was the most useless, he'll be the one getting the promotion in the end.
My version was Charlie wasn't worth paying for 9 saved minutes so I basically had the same reaction.
But if Charlie gets fired, then the equation gets screwed up and we have to start all over again!
Yes, with a little more math it comes out that Alice is 7 times more productive than Charlie & in the project with all three, Alice did 54.8% of the work, Bob did 38.5% of the work, and Charlie only did 7.7% of the work.
I looked a the original equation and said "two hours. Anne and Bob will do it and Charlie will go get them all coffee".
This is the REAL LIFE answer !! :)
I said less than 2.
Yeah definitely Considering for the fact that charlie only took off 9 minutes out of 2 hours.
but wouldn't the coffee make them work faster?
@@fnutarf2085 you assume it would take Charlie less than 1 hour 51 minutes to get them that coffee.
In one hour Alice+Bob complete half the job, Alice+Charlie complete third of the job, Bob+Charlie complete one forth of the job. Adding all that we get that in 2 hours (since each name appears twice) three of them working together complete (1/2+1/3+1/4)th of the job. 1/2+1/3+1/4 = 13/12. Set up a simple proportion: 2 hours corresponds to 13/12 job, x hours corresponds to 1 job, so x=2/(13/12)=24/13.
4.5 hours is entirely believable - I've worked with people on teams who actually slow the whole team down - also, the Mythical Manhour explains how adding more people to a problem can actually make it take longer
😂😂😂 like group study
Yeah, anybody that has worked anywhere would not have questioned that conclusion. It would have been more like, oh wow the math is actually accurate to real life for once.
Yes but they have to work at constant rate
exactly what i was thinking
If you want to get something done quickly give it to somebody who is busy 😀
"It should take less time with more people helping." As someone who works in a large corporation, I laughed at this claim.
I too see this every day. This question does not define the type of work. 4.5 hrs could be correct depending on the type of work. Since we don't know for sure, the answer should be impossible to determine without more information.
LOL, yeah been there done that, once the slackers realise they can sit on their butts, the jobs always take longer but the slackers get promoted LOL!
Its the same logic as 9 mothers can give birth in one month
Yep - people will argue and take more time - I thought that was the trick of the problem.
Just because it should, doesn't mean it will. Sadly enough.
Charlie has management written all over him.
You deserve so many more likes.
Seriously! Case in point: I drive a truck on a route servicing offices. Sometimes gal A goes with me to make things go faster. She has a lot of experience. Gal B works in the office and writes down the order in which I should service the stops. Gal B does not drive and has never ridden along in a truck to help out. Recently, I hit a stumble in the route and needed advice as to how to proceed given time and miles traveled. I called gal A to get advice. Gal A gave me advice based upon her experience. It worked out. But when I got back to the office, I was reprimanded for not having asked gal B. "Why would I ask gal B if she would have to go and ask gal A, when I could just ask gal A myself?" And, why should I burn up ten minutes trying to save ten minutes? It was reaffirmed by management that I must ask the lesser qualified and informed gal because that is her job. My take-away: "You expect me to be efficient, except when you expect me to be inefficient for arbitrary reasons."
LOL!
OK. Well I'm looking at this purely from an 'efficiency' perspective (probably comes from my time as a manager for a call center). Firstly, if they're doing the same job at a constant rate, then Charlie needs additional training or performance management, especially based on Alice's and Bob's performance together. Secondly, why has Bob become less efficient while working with Charlie? Thirdly, I will give Alice the benefit of the doubt that she's highly efficient and that Charlie caused their time together to blow out by one hour, especially as Bob's efficiency seems to have declined while working with Charlie as well.
So the common denominator of inefficiency seems to be Charlie. "Charlie, it's time to shape up or ship out".
So my answer is 2.55 hours. People will ask, "if the quickest time is 2 hours with two people, then surely with three people it has to be quicker than 2 hours"?
Not so, taking the average of 'efficiency' over the three job tasks, this brings us to an efficiency rate of 72.22% or an inefficiency rate of 27.78%. Therefore with Alice, Bob and Charlie all doing the same job task together = 2 hours + 27.78% = 2.55 hours.
Easy solution:
since, X =>2hrs for 1 work, ∴ x = 1/2 work per hr
so we can just reciprocate...
A+B=1/2 --①
A+C =1/3 --②
B+C =1/4 --③
since, eq1+eq2+eq3 = 2(A+B+C)
(A+B)+(A+C)+(B+C)=1/2+1/3+1/4
2(A+B+C)=1/2+1/3+1/4
A+B+C=(1/2+1/3+1/4)*2
A+B+C=(13/12)*2
∴Work per hr=13/24
thus, work = 24/13
now in terms of hrs & mins;
24hr 4min (approx 4 min)
“More people working on a job should get it done quicker”
The reason most college students get this question incorrect is because they understand that... No.
But that is how that works, if they are for example building/painting a wall. Everybody works on their own part of it without interfering with each other.
@@nesnasimgoogle4580 - in quite a few types of jobs, adding people increases the friction, slowing down everyone. For example, if there are only two paint cans, now Charlie must interrupt Alice and Bob to get paint. Or, at the beginning, extra time is spent to find a new can for Charlie and to fill it for him. Which, in the real world, unless you have excess amounts of paint, someone will run out of paint during the job and will need to interrupt the other two for more paint. The real world is messy; algebraic problems are simplified views of the world where these non-numeric factors are ignored.
see, when the 3 people have to build a house they take less time because one starts with the wall, the other builds the roof and the third installs window and doors. and this makes sense because it is mathematically correct 😌
@@violinyay6632 - What you described cannot all happen at once, because the guy building the wall needs to build it BEFORE the roof or the doors and windows can begin to be installed. Math IS great, but it needs to be applied carefully, taking into account the knowledge of the real world.
@@billb7636 Damn, I forgot that gravity exists again. How does that keep happening?
It's really embarassing.
You should see me trying to build with Legos
Three days. See, Bob has a crush on Alice, but Alice is hooking up with Charlie, which accounts for the extra hour it takes the two of them together and the extra two hours Bob and Charlie spend arguing. If you put all three on the same task, the dynamic totally breaks down, Bob and Charlie both end up in 48 hour lockup and Alice quits because of the 'toxic work environment'.
I smell lawsuit
😂😂😂😂 most logical response yet!
Classic! That is so funny I work with a painting crew and I tell you it is exactly as you explained. I'm the foreman and I get so frustrated because I'll put 2 guys on a job that should take a half an hour and they are still in there 3 hours later! LOL LOL
The real world intrudes again!
Hahaha ....its refreshing to run across a sense of humor similar to my own!
Insight: don’t involve Charlie in group projects
So the correct answer is fire Charlie and save some money, since his contribution only reduces the job completion by 9 minutes.
What I learned is that Alice is the GOAT and Charlie’s illiteracy has screwed us again
Yeah sure whatever but how much do you know about bird law hmmm?
Well, uh... Fillibuster?
Then Go Away! ,Finally!
Bib’s the GOAT too.
Charlie don't surf, but we think he should.
As an elementary school teacher intern, I can tell you that more people in a group can DEFINETELY mean the task takes longer to get finished.
🤣🤣🤣🤣
Hope you are not an English teacher.
It depends on the job. Lets say you are cutting a forest down. Would it be longer if you make 2 people do the job instead of 1 ?
@@smurfdurf5625 by your logic, I can tell you that it can take longer, because it also depends on who you are working with. Could be someone who distracts you, and could be a person who will help you
As a retired teacher, I miss the good old days when someone who aspires to educate children could spell common words, especially ones they capitalize.
So Charlie is just useless as a worker then.
Yeah well Wonka gave him the keys to the whole bloody factory so what are you going to do?!
Yes, he's management material.
Doug Rosengard Trick him into turning himself into a giant blueberry and then get the government to pay his unemployment benefits of course.
What it means is, chuck is a dick. That's what you hear from chucks co-workers. FACT OF LIFE. 🇺🇸
What's worse is Dwayne never even bothered to show up to work.
I went about this in a slightly different way. I thought, okay, if we assume the job is the same, then the workload is N, we're dividing that workload by the productivity of the workers, we get:
N/(A+B) = 2
N/(A+C) = 3
N/(B+C) = 4
From there, I solved the simultaneous equations to get B = 5C and A = 7C, and thus, substituting the variables:
N/(6C) = 4
N = 24C
and:
A+B+C = 7C+5C+C = 13C
And so, 24C/13C = 24/13 = 1.846...
If Charlie was left at this alone, he would take a full 24 hours to finish the job. Poor guy.
If charlie was left alone he would quit or kill himself because he's a career underachiever.
Fire Charlie. Too slow. He doesn't bring much to the table.
But Charlie is the boss...
But Charlie is the scrum master and agile mentor.
I read a comment saying that Charlie was a kid helping their parents in the kitchen, which would make perfect sense if you think about it.
Edit: Actually nvm it doesn't make sense since it says 'job' not task or whatever.
Charlie is doing the unprofitable jobs so Alice and Bob can make lots of money for the company.
My first thought when I saw this was that this is a very easy problem to solve. Charlie is holding back the other 2 employees. We need to find another task, if possible, for Charlie to do to see if he can do better at that task. But then I realized that Charlie’s feeling will be hurt if we do that so I guess the company is just going to have to add time to the assigned task so that his efficiency reaches the 100% mark.
Imagine paying Charlie's whole salary just to save 10 minutes. Guy must be friends with the boss or something.
He’s is clearly an intern that has newly arrived...
Say there were 100 people working on the project. That 10 minute early completion time now means 1000 minutes of man hours saved (assuming everyone needed to be working for the full duration), so there are some cases where it could be beneficial!
9
@@mrksgb8607 not possible, new interns can only slow down tasks
Source: currently a new intern
If I had to guess, I would say he's the owner's nephew who just graduated High School and needs to pay rent to his Dad. Just don't tell any of the other employees.
I figured it out by seeing how much each could do in 12 hours. Alice and Bob can do 6 jobs in 12 hours. Alice and Charlie can do 4 jobs in 12 hours. Bob and Charlie can do 3 jobs in 12 hours. That equals 13 jobs in 12 hours, but everybody was counted twice so its 6.5 jobs in 12 hours or 12/6.5 hours per job = 1 11/13 hour per job.
Calling the problem "basic" is an overstatement. The problem itself is tricky unless you take context into consideration, but schools do not teach this, especially in math. Students learn systems of equations, but are taught to solve problems like this as simple equations rather than worry about percentages.
I think the main issue isn't that college students can't solve this "basic" problem, but rather schools don't prepare students to solve problems like this correctly. In math, most students don't think about the context of the problem itself, but rather patterns in the problem and using equations and formulas to solve it.
can confirm, in calc 3. the extent of word problems is physics and that just supplies variables to use in memorized equations
Sry If your school was like you said. I learned in school to think before calculate, what could be a solution, and after calculation, can this solution be right.
Ok.. I plugged this into Wolfram Alpha: Alice is 7/24, Bob is 5/24 and Charlie is 1/24. Charlie should save 10 minutes off the job (1/12 of 60). It’s almost like an “are you smarter than a 5th grader question”. But I do agree though, schools teach too much by rote.
Not idea where u studied, but at my highschool I have done many problems like this in classroom lmao. it actually surprise me that college students are having problems with this kind of basic equation.
As a college student, this is definitely very true
Well, Alice and Bob have good chemistry together, so they get the job done fast. Alice and Charlie don't mind each other. Bob and Charlie actively dislike each other, so when they all group up to get the job done, Bob says: "Charlie, no offense, but me and Alice alone would get this done faster than if you weren't here, so go do something else."
2 hours.
Alice and Bob actually finished the job in 1 hr 55 mins. But they clocked at 2 hrs just so they can beat Charlie up for 5 mins straight
This is exactly how it goes in the real world.
Except the beating.
It's a lot more fun to watch Charlie struggle for 5 minutes trying to tie his shoes, only to finally manage it and realize he put them on the wrong feet.
I definitely read it as Bob and Charlie were buds and just goofed off the whole time.
@@datphung8656 I died laughing at this and the comment above.
@@frisbeedan8905 Yes; me too. Charlie is a fun guy and even Alice laughs when she works with him.
Adding Charlie to the team saves 9 minutes, because he is able to fetch coffee for Alice and Bob.
What I thought. Alice and Bob do the job and tell Charlie to keep out of the way unless they want him for something.
Charlie felt demotivated as he missed Chaplin at Work😆
I'm feeling real sad for charlie...
Nah actually Alice and Bob wanted to finish the work so they send away Charlie to get a coffee and the guy disappeared for almost 2hours, they finished early because they where thinking of finding him to see what he was doing, they just didnt do it before because they wanted to at least finish the job
Charlie work
Intuitively, the best way to understand it is by calculating how many times each combination can complete the task in a 12 hour period (12 is a common multiple of 2,3,4)
A+B=6 A+C=4 B+C=3 therefore A=3.5 B=2.5 C=0.5 and A+B+C=6.5 so we convert it back into our 12 hour period: 12/6.5 = 1.846... = 1h50m46s
The answer is that Alice should be promoted and Charlie should be fired!
So you want to promote the worker who is best at the current job and slow down your production. Why not promote Charlie he might be a fantastic manager
You're wrong about Charlie. It took him only 9 minutes to do the job and get it right. It took Bob 2 hours hours but left everything screwed up. Alice didn't do sh!t. Nympho Alice distracted Charlie so it took him 2 hrs and 51 min of fighting off Alice. Charlie had to spend 3hrs and 51 minutes correcting Bobs mistakes. Charlie was able to complete the job correctly in 9 minutes but it took 1hr and 42 minutes trying to get Bob and Alice out of the closet.
What about bob? What’s he been doin’? Bob’s a weirdo
Ahahahahahahah
Reply give me a good laugh 😂😂😂😂😂😂😂😂
Real world answer: Alice is an ISTJ and can get the job done in one hour if the other two, and everyone else, would just leave her the hell alone.
@@tarico4436 Random misogynistic incel comment right here folks, *claps*
How's therapy going?
@@tarico4436 YIKES
I never heard of ISTJ before, I read about it and it sounded like me (which I expected after this comment). So I took an online test and it told me I'm an INTJ, I wasn't sure which one fits more to me so I did another online test and again ended up as an INTJ. But I still think that depending on the situation I'm something in-between.
Yeah, based on those numbers, Alice can do the job alone in 3.5 hours (which is less than the other two together), Bob can do it in about 5, and Charlie left to his own devices would need 24 HOURS!!! Let the woman do her thing!
I had a simple answer: Charlie slows people down, so he needs to sit back and let Bob and Alice get it done the fastest, in 2 hours. We also just have to keep Bob focused because according to his work with Charlie, he gets distracted easily and takes the longest in the combo
hahaha exactly, I think so too
Charlie doesn't slow things down he just works more slowly but is still making progress, not slowing it. Letting Bob and Alice do it alone is 9 minutes SLOWER than if Charlie helped.
As somebody who used to work in retail management, this is the correct answer. Charlie should be assigned to a different task that will allow him to work at his own pace or one that doesn't have to be perfect, but is repetitive, and he can rush through to get it done.
@James Ratliff Alice should work alone instead.
Charlie had special needs and discrimination will not be tolerated. Now Alice and Bob both lost their jobs because Charlie viewed Alice and Bob's comments about "working too slow" as harassment. Now the whole operation is run by Charlie. Moments later, everything has been outsourced to a disadvantaged country to avoid bankruptcy. Everyone loses their jobs, and Charlie is the only one qualified to receive social assistance because he has special needs.
An improved explanation of my (earlier) 'equivalence & comparative efficiency' solution:
The average 'completed task' contribution = 4 hrs. apiece for A & B (2 hrs. combined) / 6 hrs. apiece for A & C (3hrs. combined) / 8 hrs. apiece for B & C (4hrs. combined).
C'quently & importantly, A B & C can be dealt with as 3 individuals who are simultaneously completing a task that - separately - would take 4 6 & 8 hrs. respectively.
Based on A: B's efficiency = 4 × 4/6 = 8/3 & C' s efficiency = 4 × 4/8 = 2 such that - working simultaneously - A B & C would take 4 ÷ (4 + 8/3 + 2) times as long as 4 hrs., in completing the task.
Specifically: 4 ÷ (12/3 + 8/3 + 6/3) = 4 ÷ (26/3) = 4 × (3/26) = 12/26 -- i.e. -- would take 12/26 of 4 hrs. = 48/26 = 24/13 hours. (Working in combination @ their individual efficiency rates.) Rgrds. - R.G.S.
It amused me to work out that Charlie by himself would have taken 24 hours of continuous work to complete the task
Work is a very strong word for what this Charlie does
We all know a Charlie, we've all had group work with one
Charlie sent me an email from Goa, asking me to wire him some money for a plane ticket home. I bought him the ticket instead. I don't trust him enough.
@finger speak Indeed. Especially since Alice and Bob both probably hate Charlie for being the load.
@finger speak if we were resolving this problem with physics methods WE would take in count one more parameter to describe this "group is slowing down individual values" thing
My daughter, when she was at UGA, found it saved time when assigned a group project, to just say she would do the entire project herself. That was after a group she was in was unable find time to meet together to finalize a report, so she had to complete everyone in the group’s assignment the day before it was due. The person who commented that Alice could have done it faster if the guys would just get out of the way was right.
I detested group projects. One professor had us anonymously submit grades and evaluations of the other group members. My group was three women and a VGL guy who always made sure we knew he was going to be late for a date because of our meetings. I was the only one who submitted an honest evaluation. The professor gave the women As and Casanova a B. Everyone was shocked and wondered why. 😈
Pretty much
My daughter was a straight A student and she hated it when teachers assigned assignments to be done in a group because other students never did any work they just fooled around and she ended doing the whole thing to just get it done. She always carried the load and the others took advantage of the situation and got a better grade thanks to her efforts. Most students have a very poor work ethic and never get down to business to complete anything.
@@patsmith5947 But this is exactly how the real world works. The reward for doing your job well is always getting to do somebody else's job and if you don't know who's job you're doing....somebody is doing yours.
Go Dawgs!
I'm guessing Charlie is the son of the owner and gets promoted to manager, Bob gets promoted to supervisor and tries to employ as many Alices as he can find to get the job done.
Bingo, real world answer.
Good, I need a job.
MACKENZIEEE
I just made the job concrete. They had to move 24 boxes. This showed me that Alice moves 7 boxes per hour, Bob 5, and Charlie a measly 1. So in total they can move 13. Then it was just dividing 24 boxes by the 13 per hour.
Charlie is now a member of Congress, and considered a rising star
Nope, because Charlie has the key to the toolbox. Bob and Alice are the only people who can read the blue prints for the job.
🤣🤣🤣🤣🤣🤣🤣
You fire Charlie....problem solved!
@Mike 🤣🤣🤣🤣 no mercy!!!
Never heard Chuck Schumer referred to as Charlie but its starting to make sense now
Title: Most college students can't solve this problem
Me with a college degree: *Sweats nervously*
9 women can have a baby in one month, clearly
They have 1/9 of a baby each
If they are conjoined nonuplet sisters ... maybe? But Csection would be difficult and birthing canal obviously impossible. Unless it was human centipede set up and not some giant fleshy leg ball. Also assume genetics didn't prefer twins or greater which obviously would decrease the effectiveness of this freakish uber-womb, and break all known laws of reality TV baby shows. Causing mass hysteria, looting, etc! And of course , to top it all off. It's just crazy to think 9 bitchy pregnant woman could stay that close to each other for even a month without some poor sap walking by and finding out just how much they hate men, or anyone trying to touch their babybump. Dead . Dead by nonuplet stabbing. ...
No this would not work.
Also,
I've decided that I may have given this too much thought.
@@nh978 also gestation is 39 weeks so closer to 10 months
n dang it .... the creature cant take much more math changes , before she/they mutate, and things really get out of hand. I figured confidence would carry success forward. Not any more, thanks!
Lol. Jk
The visual haunted me for a couple days after I posted. Btw.
It's some SCP stuff for sure.
😆😆😆
5. Alice and Bob spend 3 hours trying to explain Charlie's part to him and then decide to just do it themselves.
Alice and Bob should lock Charlie in another room and they would probably do the job in under 2 hours because they did it before in 2 hours, that means they know what to expect and do it a little quicker. So I came up with 1 hour 52minutes. 1 minute longer than your solution because they had to shut Charlie up from banging on the door.
Yeah, but you KNOW Bob and Alice are going to start getting it on, I mean Alice is sooo easy. The next thing you know the whole afternoon is shot and Charlie gets blamed because he's the slow one. Alice will get promoted and Bob will be overcome with guilt for his decision to sleep with Alice and confess to his wife. His wife will make his life a living nightmare until the marriage ends in divorce and he finally spirals into a well of depression and drinking and ultimately the loss of his job. Alice will fire Charlie and replace him with a minority who can easily get the job done alone in 20 minutes but has no real incentive to do so due to low pay and discrimination. In the end, the new hire slips on his way into the building and sues the company into bankruptcy.
So Alice, Bob and Charlie can get the job done in infinite time...final answer.
Charlie knows he's being paid either way and now he's alone in a room with his phone. He's not banging on anything except himself.
@@ProfessorOzone Definitely not the final answer. When Bob and Alice get married, they will have 2 children who will grow up and do the work for them. Ha! Ha!
@@gardeningdianne they will name those two children after themselves, thus the cycle continues...
Wait no
@@chrisweyers4764 Oh Dear! We've just created another problem. I wonder what country they are in Mmm! maybe America, in which case problem solved. They could be called Bob I or Bob Junior and the same for Alice, wait a minute, I have never heard women with the extended title before, except for British royalty. Oh Dear! the problem gets deeper.
The "work done per unit of time" is the inverse of the time used to complete the work, so it is possible to just simply solve:
a + b = 1/2
a + c = 1/3
b + c = 1/4
summing up all three equations: 2a + 2b + 2c = 13/12 --> a + b + c = 13/24. The solution is the inverse of it, that is 24/13.
Holy carp this is so elegant it beats the video's "official" solution!
Yes! Much clearer to think in terms of rates.
Also thought of this in terms of rates, starting with making 120 widgets, A+B make 60/hr, A+C 40/hr and B+C 30 Hr. Adding the first 2 together 2A+B+C=100, we know B+C=30 so that means 2A = 70, or A=35 per hour simple maths from then on gives B at 25 per hour and C at 5 per hour or 65 per hour aggregate. 120/65 = 1.84 hrs (1hr 50min 46.15 sec approx.)
Yes, it is easier to assign variables to the entire individual rates, not just the individual hours. Excellent, Michele! I used Substitution while keeping everything as a fraction leaving out a discussion of percentages, which can be confusing for many students. This also was a much quicker process.
I hope you teach Math or Physics or something because your students would be blessed to have you as their instructor.
Easiest solution
I don't know how but I almost got this answer by doing the common mistake version but using reciprocals but then I flip the reciprocal and got the wrong answer. I don't know how this happened.
"Now, before I solve this, let me talk about a common mistake. Many people see the first line and translate it to A+B = 2." -> Sad me looking down on my paper. First line: A+B=2
Me too😄😄
Saaaaame 😭
Yep, same 😞😁
Ha, I fooled him, I had X+Y= 2
Same
Even before doing any math, I can safely say Charlie should probably be fired. Bob is probably an average worker, and Alice should probably be promoted or given a raise.
No, Alice's reward is more work with no raise. That's how things work. And Charlie gets promoted to manager.
@@rodicow3491 That is the way the real world works, the real worker gets all the S@h@t rolled down on himself while the others get praswd and paid more to do less work.
@@rodicow3491 sounds like Charlie is the son of someone in upper management.
@@piranhaplantX Or the manager's friend from church/book club etc. We've all worked with the type XD
Charles is the intern.
Sounds like Charlie needs to be fired and Bob needs to have little meeting with HR and Alice she needs a raise maybe a bonus too!😙
We dont know that. May be they are all ridiculously slow. Was the job to wipe off a small table ?
@G Sav Sounds about right lol.
@G Sav vicious, man, vicious.
You going to get copyright on that before Hollyweird steals it? 😜😜🤪🤪
That's what I said too! Lazy ass sounds like..charlie slacker :)
@M Pr I said something similar lol
The thumbnail is Alice = 0.5, Bob = 1.5, and Charlie = 2.5, so altogether they are 4.5.
I tried doing only the problem on the thumbnail only for the video to just tell me I'm wrong because it's a different question 😭
@@realmeme6 Yeah, that happens to me quite a bit 😅
4.5 could be possible. I know many people who's work potential is negative...
Especially when in groups, some tend to become freeloaders.
That’s exactly what I got
*whose
Video is to long.
They work at steady rates
You're telling me that Charlie saved a measly 9 minutes in a two hour project...
He might be in training
@@potato1341 or maby he isnt a team player so the whole team wil loose time for completing the work
I've known Charlies who added minutes to the project...
My name is Charlie ¯\_(ツ)_/¯.
@@greenjelly01 dude i died laughing 😂😂
This logic went out the window when you realize adding a third person only saved them 10 minutes.
its because Charlie is useless. He's 7 times slower than Alice and 5 times slower than Bob. He hardly makes any difference.
I've met so many Charlies...
Not even 10 minutes. In real life you will spend more time explaining it to Charlie than he will actually do. He must be the boss' son.
I have experienced this directly when running a landscaping crew in my twenties, myself and my co-crew lead could get a yard done faster alone than with a crew of four. We would have to delay and wait for the others to finish their tasks before we could proceed with ours. After a week we tried dividing the teams, dropping one of us off with one of the others at one yard and then whoever was driving that day would take the other crew member and do another yard, this took even longer, week 3 we dropped the other two off and went and did on average two yards before they would finish one, at the end of week three we fired the other two and gave our selves a raise with the savings from their wages.
It is because the statement of the problem is incorrect. Switch Alice and Charlie, and now Alice is the useless one.
i've seen glaciers move faster than Charlie
Way to make a problem way more complicated than it needed to be.
Convert from times to rates: A+B=1/2; A+C=1/3; B+C=1/4 [all in jobs per hours]
Add up both sides of all three: 2(A+B+C)=13/12
Simplify: A+B+C=13/24
Convert back to time: 24/13 [back to being hours]
Yep, much simpler. The maths is technically identical, but much easier to understand each of the subsequent steps after you make the initial conversion.
Yes, jobs-per-hour is the key concept, gives 3 equations for 3 unknowns, better to solve them as such, rather than looking for a trick, in this case adding all 3 equations, which works in this example, but might not work in other examples.
@@climanrecon5649 well adding all 3 equations is just a shortcut to forming a quantity proportional to A+B+C. In either method it could be done by individually solving for A, B, and C, but that's more work than is necessary
This was the way I did it, the part of the question saying “assume all work at a constant rate” saved me from falling into the A+B=2 trap
@@thomasr5302 Assuming constant rates is a good clue, but it leaves out a critical assumption: that there are no interactions (in the statistical sense). In other words, we must also assume that each person works at the same rate regardless of who else is working with them. As a real-world counter-example, my guess is that it would take the three of them about 24/7 hours to do the job as a trio, because Alice would end up doing everything while Bob and Charlie worthlessly compete for her attention.
6 hours. Seeing how the time takes longer with Charlie working, and less with Alice, its obvious Alice is grounded and Charlie screws around. Bob is gonna get pulled into Charlie screw around and Alice will take longer trying to get the other two to work
I worked with Charlie and I know this is a fact. Charlie has ADD.
i feel like im Alice
My mind went to Harry Potter.
this is the most sensible answer
Charlie's 1hr51min of work was equivalent to Alice's 9min + Bob's 9min.
Charlie should be fired ASAP.
Sadly this is a very common occurrence in fast food jobs. You'll always have a couple hard workers and a BUNCH of lazy bums that make the good workers seem bad too. Its harsh to work your ass off and then get told by customers that you're paid too much.
Bob is 5 times faster than Charlie and Alice is 7 times faster.
So, 1hr 48 min of Charlie's work is equivalent to Alice's 9min and Bob's 9 min.
Charlie's work of 1hr51min = 111 min. Alice will get that job done 7 times faster = 111/7 = 15 minutes. Bob will do that 5 times faster = 111/5 = 22 minutes.
Alice and Bob dividing that job will do it 7 + 5 = 13 times faster = 111/13 = 8.5 minutes
I assumed that it was some sort of household task and Charlie was their child 🤷
Send Charlie out for lunch, he's buying.
My teacher taught this to me when I was 12, shame I lost track of it... Guess I got to brush back up. I only knew that it'd be quicker, but not by how much...
My silly way of thinking about it:
If A & B can do it in 2 hours, then they can do it 6 times in 12 hours.
If A & C can do it in 3 hours, then they can do it 4 times in 12 hours.
If B & C can do it in 4 hours, then they can do it 3 times in 12 hours.
So A & B & A & C & B & C together will do it 6+4+3=13 times in 12 hours.
That's two of each person, so one of each will take double the time:13 times in 24 hours.
If it takes them 24 hours to do it 13 times, then it takes them 24/13 hours to do it 1 time.
What do you mean by "thats two of each person, so one of each will take double the time", do you mean that because since its pairing, you times the fraction by 2 because you divide the pairing to make it 1 person?
@@luminesent I mean that 2A, 2B, and 2C, will finish the task in half the time as A, B, and C will. Exactly double the people means half the time taken.
Not silly at all. This is a "verbal reasoning" representation of what Presh says with mathematical equations. It may well be a better representation for many people.
@Awesimo he is the chosen one and he shall be called Awesimo!!!
This approach makes it easier for me to understand. Finding the common denominator first is making the whole thing easier to conceptualize. Before I watched the explanation I was trying to solve the problem with averages, but I ended up with an answer of one hour. I knew I was doing it wrong. You should teach math if you don't already.
Being a contractor, I came up with about 11/2 hrs. unless it’s a union job then I figure it will take a week counting lunch breaks and coffee breaks with phone calls and bathroom breaks thrown in . Good luck 👍
I love being Union. More pay and benefits. Sorry if you all work like dogs, and only take home scraps.
@@romanticdonkey468 - and you have the Unions and the Democrats permission to say so. At least I can vote for who I choose!
LOL...my answer is 90min
Up yours Ron, if employers would have treated their workers fairly from the start unions wouldn't have been necessary. If your union workers have that many perks then it is your own fault for not being smart enough at the negotiation table. GO Union strong. Teamsters 0471.
@@chezman3892 - when I was in a union, it was the PBA , money for nothing as far as our dues, like today all they did was role over and play dead whenever our contracts came up. If you’re in a good union more power to ya mine pretty much sucked.
It will take 2 hours . Alice will do the work, Bob will help and Charlie will watch. End of story.
Alice will do most of the work, Bob will help somewhat but mostly get in the way, Charlie will spend the two hours taking credit and brown-nosing the boss and will get promoted before Alice or Bob. Then he'll continue to give them all the work.
Alice and Dilbert (Bob) work together while Wally (Charlie) drinks coffee and reads the newspaper in his "office." After much labor the PHB informs Alice and Dilbert the project was cancelled a couple of months ago due to a reorganization. So Wally turns out to be the only winner here...as usual. So C>(A+B) and PHB
It just takes one hour for Alice to finish the work alone.. The other two douchebags are slower..
@@pragalpaah4314 Of course!. If Alice is alone, she doesn't get distracted. If she works with any of them, she does. Don't you see the problem? Is called hormones.
Alice and Bob will do the "work." Charlie will watch.
Fixed your story.
I solved this by effectively using the parallel resistance formula: 1/A + 1/B + 1/C = 1/t, solve for t.
I came up with this by realising that, instead of adding the times, I should be adding the speeds. And since speed = distance/time, I set distance to 1 and added. Then, since time = distance/speed, I did 1 over the total and got 24/13. You can use any positive number in place of 1 and it still works.
Fabulous 🎉
2 hours and 15 minutes. (It takes 15 minutes to have Charlie clean out his desk.)
Charlie is gumming up the works 🙄
I have stupidvisor that doesn’t understand this concept.
Charlie? Bob's the slacker. On second thoughts, maybe Bob fancies Alice, and not Charlie, so when he works with Alice he's trying to impress. Whereas when he works with Charlie, he's trying to get him fired so he can work more with Alice.
@The devil is in the details I see what you did there.
As a result of this, Charlie is promoted to management.
Failing up is the American Way.
Golden formula no work no mistake.
Since he is not pulling his weight in that position, it only makes sense to make him useful in more better position higher up. /s
@@myrmaad or any government. My wife works in care in the community and her current director of service has failed and been moved around for the best part of 5 years. The manager is still crap, but higher paid crap. She works for a local metropolitan council in the UK.
BS! You are mistaken...Charlie should be fired.
Great video! However, regarding "Does this answer make sense?" As an engineer, I promise that it is entirely possible that adding "helpers" can increase the amount of time it takes to complete a project, especially when it's done late in the game in an effort to correct a slipping schedule.
Yep. That has been my experience in SAP Functional for projects when management assumes throwing people at it will reduce the time at the same rate. The same logic that killed 60k British soldiers at the Battle of the Somme during the first day. Real life is never the same as theory, and people need to respect the realities of human nature and the limitations of scare resources with alternative uses.
Yes I agree but the the condition of the problem stated that working together or alone does not increase or decrease the rate of work done.
also known as law of diminishing marginal returns
Especially if the additional people continually insist on "revisiting" everything that has already been decided.
@@ghost307 LOL. We'll circle back and drill down on that.
Charlie is an intern. He doesn't really know what the job is.
Or a nepotism hire that doesn't know how to do the job and forces everyone to do the job his way (AKA the way that takes 5 times longer).
The first answer makes perfect sense if you are contractor.
- "How long time will it take?"
- "It will take two hours for me to do it. If you want to help, it will take four and a half hours."
And if you want a govt grant/blow out your budget, and take a couple of years, put together a committee and we'll get right on it.
The solution is to let Alice do the work alone.
If Bob is getting in her way, it takes her 2 hours to overcome his antics.
If Charlie is getting in her way, it takes 3 hours for her to fix his half baked semi-effort.
So it's a bloody miracle that when Bob and Charlie toss the towel into the ring and call it quits after 4 hours that anyone would consider that work being done.
Alice could probably sort the thing out in 30 minutes or so, it's just those blokes getting in her way that mess things up.
My estimate was she could do it in 1 hour, but it depends
Alice alone would take about 3 hours, 25 minutes, and 43 seconds to do the work.
Alice does 7/24ths of the work per hour. T(Alice)=24/7 hours to be exact
@Fermitu Actually they said the rate of work of every person is same if they work with or without others. So it can't really work like that
@@shkhrvarshney precisely. Alice does the job in 30 minutes by herself. Since we were never given an individual initial condition of how the people work when they work alone we don't know whether Bob adds time to the job. He might have different requirements for what needs to get done or simply complete his portion of the job that much slower. Alice does her work in 30 minutes and stops because she has other things to do. Then Bob works for another hour and a half to fill out his timecard.
@@shkhrvarshney that way regardless of who they work with Alice consistently completes the job in 30 minutes, Bob takes an hour and a half, and Charlie takes two and a half hours.
The answer is simple, workers Bob and Charlie are fired, Alice now has three times the workload and quits.
Infinite time required for all three as none are working there any more.
No, fire Charlie, give Alice the raise she deserves, hire an intern to replace Charlie and have Alice train them,, and tell Bob if he doesn't pick up the pace, he's not getting his production bonus
@@kenworthcowboy9739 In the "real" world, Bob and Charlie are fired, Alice is given the additional workload but no increase in pay. Then, she quits. Been there - done that.
@@MasterYoist whomever was in charge of that office is the one who needed to be fired!!
Nah, open a plant overseas where you do not care if it takes 10 hours for 6 of them to do the job because labor is so cheap. Promote Alice to go overseas and train the employee at the new plant on a 6 month agreement but do not renew her term.
Bob's not that bad - he's about 70% as efficient as Alice. Not worth firing him over.
I did not figure this out. I am a 58 year old man with minimal education who failed high school math. But I realized almost immediately that the answer must be a little less than 2 and then I got hung up on whether the answer should be expressed as a fraction, or as a decimal.
if you've ever owned a business and employed people, 4.5 hours is correct.
Seems like Alice does all the work, while bob and charlie discuss how to do the work. ;)
Soooo true!
Yep, when real life and theory don’t equate.
@@user-unknown173 probably due to the law of diminishing returns which states that if a varying factor (in this case the number of people working) is increased to a fixed factor (the room they work in or something) the returns (the hours they take) will decrease (increase in this case) as the variable goes too far. This is not a math thing its actually a business thing. Thing like what happens when a balloon (the fixed factor) is blown (the varying factor) too much.
Me: yay it’s the holiday!
Also me: watches maths problem at 3am.
Lol same😶
tbh,watching a math while in holiday is waay more relaxing
because you there isn't a deadline and assignment to do
Same for me except its quarantine due to corona
@@abysswalker2403 expected at least one corona reply
Alice is so smart that she makes the manager feel threatened. She takes on so much work and expects compensation but they decide not to give it to her because then it would affirm that she is too good for the job and management. So they keep her wage low until she gets upset and leaves. Leaving Bob and Charlie with too much work and a failing company. Should have just paid Alice what she was worth because now everyone loses.
Correct!
And THAT’S the reality in Corporate America.
Yes indeed. Alternatively, they tell Alice "Sorry, we don't have the budget to give you a raise. You need to be a team player and suck it up for the good of the company. By the way, here's some more work." Alice quits and the company then hires three people to do her job.
I feel as though I'm living this
@@GayleHallAZ *situation or state, not "the reality."
The vile phrase "the reality in X" is a generic mouth-breather misuse of the word "reality." Misusing as if it means "a given or personal situation."
Reality is not a plaything, there is only one and it is absolute; we play within it. We can never compartmentalize~control anything but our opinion regarding reality. Means there is no such thing as "realities" for that makes them all falsehood~belief and not actual reality; *the singular~universal substrate of all other things*
Alternative way:-
We know,
Efficiency( rate at which work is done by one) and time are inversely proportional to each other.[ i.e. The more someone takes time to finish a job, the less efficient he/she is and the less someone takes time, the more efficient he/she is.]
Time taken by Alice(A) and Bob(B) to complete the job= 2 hours
Time taken by Alice(A) and Charlie(C) to complete the job= 3 hours
Time taken by Bob(B) and Charlie(C) to complete the job= 4 hours
Work done by A and B in 1 hour= 1/2
Work done by A and C in 1 hour= 1/3
Work done by B and C in 1 hour= 1/4
Work done by 2(A+ B + C) in 1 hour= 1/2 + 1/3+ 1/4
=13/12
Work done by (A+ B + C) in 1 hour= 13/12* 1/2
= 13/24
Hence,
time taken by Alice, Bob and Charlie to complete the job is (24/13) hours.