Tom can do a job in 4 hrs. With Sam’s help it takes 2 and 2/9 hrs. How long will it take Sam alone?
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- Опубликовано: 22 янв 2024
- How to solve an algebra work word problem.
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Tom's jobs/hr: T = 1/4. Let Sam's jobs/hr = S. Working together, their jobs/hr = 1/4 + S. The time required for one job is the reciprocal of that combined rate: T + S = 1/(2 2/9) = 1/(20/9).
So, T + S = 9/20. Solve for S: S = 9/20 - T = 9/20 - 1/4 = 9/20 - 5/20 = 4/20 = 2/10. The time required for Sam to do a job is 1/S = 1 / (2/10) = 10/2 = 5. Sam gets it done by himself in 5 hours.
I went about this somewhat differently.
The first thing I did was to turm Sam's rate of work into job hours.
I did this dividing 1 by the number of hours Sam took to do the job.
Tom works at the rate of 1/4 job hour.
I then figured out the number of job hours both Tom and Sam work at, combined.
I cam up with 9/20 job hour with both of them working on it.
I then converted the number of job hours Tom works at to 20ths of a job hour, and I got 5.
I then subtracted 5/20 from 9/20 to get 4/20 for Sam's work rate. So Sam works at 4/20 job hour whic is the same as 1/5 job hour.
Kind of depends on the job. These kind of questions always assume that working together is just two people working side by side separately but it's odd because almost no job is like that.
Tom labor power is T and Sams is S. Time is in numbers 4T=C complete or (T + S) *20/9 =C Set 4T= (T+S)*20/9 Now 36/9*T= T*20/9 +S*20/9 Now T*16/9=S*20/9 4T=5S So in four hours Tom does the same work as Sam does in 5 hours. No need to remember special formulas. Just write out what you know algebraically. This makes sense because Sam is obviously not as fast as Tom because when they work together they don't complete the job in half the time and we don't know anything else about the job. Toms labor power is greater than Sams. 5S=C
Now in mathematics, anytime we are dealing with word problems, we will be dealing with words...
Sam's the labourer. He's fairly quick and efficient but not without Tom. He can't do the job.
Answer is 5 hrs - Dr. Kapadia
3&1/9
I think Sam can do the job in 5 hours, working alone.
So who has got a watch calibrated in ninths?
4 4/9 hrs
So 4 hrs is 36 9ths, 2 hrs and 2 9ths is 20 9ths. So with Sam's help, Tom did 20 out of 36 9ths of the work so Sam did 16 9ths of the work. So Sam's work rate is 16/20ths of Tom's =4/5. So his time taken to do a job will be 5/4ths of Tom therefore 5 hours. Entirely possible of course that Sam night not be able to do the job at all without Tom....
1:70 2:10hours.
5hrs
Sam works on it for several hours and totally botched the project since he doesn't possess the necessary skills to complete the job accurately. Subsequently, he heads to the bar to brag to his friends how GREAT his work was only to be confronted by the irate customer demanding he return to redo the work. In order to save face, SAM deny's yhe accusation and tells the Owner to bugger off while announcing to the bar, "This round is on me!" After a room full of cheer, Sam loses himself in the crowd and makes his way toward the door.
How much money does Sam owe the bar and how fast does he have to run to avoid payment?
How come I got 4 hours and 45 minutes (Sam working alone)?
dunno! you didn't show your work for partial credit
Show us what you did and then we can tell you.
I did get the answer .. 5 hours .. but, to be quite honest, I'm still trying to get my head around 2/9 of an hour 🤔
It isn't even a whole number of minutes.
Well it's 6 minutes and 40 seconds... clearly not a quantity that anyone would refer to. But it makes the answer a convenient whole number.
@@timothybloomer8287 I do realise that but I honestly think that the only three fractions that are OK to use when you are talking about 'parts of an hour' are 1/4 past 1/2 past and 1/4 to
.. and don't even get me started on what I think about expressions like 2.7 hours 🤐
Maybe I'm just getting old 🤔 .. you know .. back in the days when clocks actually had hands and you had to work out whether it was 17 or 18 minutes past the hour 😛😜😝
Grumpy old man !!
In 1 hr Tom can do 1/4 of whole job all by himself. Tom and Sam together can finish 9/20 of the job in 1 hour. Hence, Sam can finish 9/20 - 1/4 = 4/20 = 1/5 th. of the job in 1 hour. Hence, Sam can do the job in 1/(1/5) = 5 hours by himself. ✌️
Don’t know Sam and Tom are Homeless and we’re digging a cave in California and the city shut them down.
It is not known whether or not Sam can do the entire job alone. It only states he is a helper.
Since it asks how long it takes Sam alone, there's an assumption he can do the entire job alone. No smiley face for you. Come back one year.
@@terry_willis You present a logical fallacy. One should never draw assumptions like this in science or logic. The question is badly written. I agree with the OP.
What you're forgetting is that Sam can't do the job without Tom, because Tom owns all the equipment which he secures in a lock-up when he's not working.
Dry joke
1 job / Speed Tom = 4 hr so Speed Tom = ST = 1/4 job/hr or ST = 1/4 (1)
Speed Sam = SS is to be found...
1 job / Speed (Tom + Sam) = 20/9 job/hr or 1 / (ST+SS) = 20/9 (2)
(1)+(2): 1 / (1/4 + SS) = 20/9 so 1 = 20/9 . (1/4 + SS) -> SS = 9/20 - 1/4 = 9/20 - 5/20 = 4/20 = 1/5 job/hr
So Sam will take 1 job / 1/5 job/hr = 1 job . 5 hr/job = 5 hours.
Same principle: Alex and Bob will do a job in 2 hours, Alex and Charles will do the same job in 3 hours, Bob and Charles will do it in 4 hours... In what time will they do the job if they work all together?
A = speed Alex, B = speed Bob and C = speed Charles
1 job / (A + B) job/hr = 2 hr so 2(A+B) = 1 or A+B = 1/2 job/hr -> A = 1/2 - B (1)
1 job / (A + C) job/hr = 3 hr so 3(A+C) = 1 or A+C = 1/3 job/hr -> A = 1/3 - C (2)
1 job / (B + C) job/hr = 4 hr so 4(B+C) = 1 or B+C = 1/4 job/hr -> B = 1/4 - C (3)
3 variables and 3 equations so this can be solved !
(1)+(2): 1/2 - B = 1/3 - C so C = B + 1/3 - 1/2 = B + 2/6 - 3/6 -> C = B - 1/6 (4)
(3)+(4): B = 1/4 - B + 1/6 so 2B = 1/4 + 1/6 = 3/12 + 2/12 = 5/12 and B = 5/24 job/hr (5)
(1)+(5): A = 1/2 - 5/24 = 12/24 - 5/24 = 7/24 job/hr (6)
(2)+(6): C = 1/3 - A = 8/24 - 7/24 = 1/24 job/hr (7)
(5)+(6)+(7): A+B+C = 13/24 job/hr
So 1 job = 1 / (13/24) = 24/13 hr = 1 hr and 60 . (24-13)/13 minutes = 1 hr and 60 . 11/13 = 1 hour and 50.77 minutes
= 1 hour 50 minutes and 60 . 0.77 seconds = 1 hour 50 minutes and 46 seconds.
Alex and Bob did the job in 2 hours, adding lazy Charles only limited the work time with about 9 minutes.
If Alex would do the job on his own he would need 24/7 hr ~ 3 hours and 26 minutes
Bob will need 24/5 hr = 4 hours and 48 minutes
Charles will need 24/1 hr = 24 hours...
such a rubbish question .. what happens at the point in the job when you need one person at one end and another at the other while one can mark off ... no wonder some kids fail these things ; they can't compensate for your missing knowledge
two unknowns
S Sam's rate of work
T Tom's rate of work
givens
Tom's task completion = 4hr
Tom + Sam completion = 2&(2/9)
find:
Time for Sam to do job alone
two equations
T = 1 Job/4Hr
= (1/4) Job/Hr eq.1 [0.25]
S+T = 1 Job/(2&(2/9))Hr
= 1 Job/(20/9)Hr
= (9/20) Job/Hr eq.2 [0.45]
S+T= (9/20) Job/hr
so
S = (9/20) Job/Hr - T Job/Hr
T= (1/4) Job/Hr
so
S = (9/20)-(1/4)
= (9/20)-(5/20)
= (4/20)Job/Hr
= (1/5) Job/Hr
A complete job for Sam
= [(1/5) Job/Hr]^(-1)
= 1/[(1/5) Job/Hr]
= 5 Hr/Job
Answer S is 5Hours/Job
alias 0 2 Job/Hr
Verify
S = 5 // 0.2
T = 4 // 0.25
S+T=? (9/20) Job/hr
0.2 + 0.25 =? (9/20) Job/Hr
0.45 =? (9/20)
0.45 =❤ 0.45✔️