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Q: If Sam can finish a job in 3 hours and Mark can finish a

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New post 12 May 2005, 16:56
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Q:
If Sam can finish a job in 3 hours and Mark can finish a job in 12 hours, in how many hours could they finish the job if they worked on it together at their respective rates?

(A) 1
(B) 2 2/5
(C) 2 5/8
(D) 3 1/4
(E) 4

What may be different ways to solve this?
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New post 12 May 2005, 17:06
One way:
Combined rate = Rate of 1 + Rate of 2
= 1/3 + 1/12 = 5/12
Therefore total time taken = 12/5 = 2, 2/5 hours

Another way:
Mark does the job in 12 hours. Now he adds someone who can do the job in 12 hours, ie 4 times faster than himself. Thus, the rate of job being done should become 5 times faster than before, and time should decrease 5 times. Therefore, total time = 12/5 = 2, 2/5

Another way:
San does the job in 3 hours. Now he adds someone who can do it at 1/4th the rate. Thus his rate increases from 1 to 1.25 and time should therefore decrease 1.25 times. Therefore total time = 3/1.25 = 2.4 = 2, 2/5

Another way:
In one hour, Mark does 1/12th work, and Sam does 1/3rd = 5/12th work.
Therefore number of hours required = 12/5 = 2, 2/5

Hope that helps.
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New post 12 May 2005, 18:06
Yes, this definitely helps. In the last method, why is 5/12 flipped to 12/5? Thanks.
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New post 12 May 2005, 19:03
above720 wrote:
Yes, this definitely helps. In the last method, why is 5/12 flipped to 12/5? Thanks.


The "flip" accounts for hours and "proportion of work done".

Simply put, if you do 1/2 of the work every hour, you take 2 hours to do it all. Or if you do 1/3rd of the work every hour, you take 3 hours to finish it all.

So since Mark and the Sam do 5/12th of the work every hour, they take 12/5 hours to finish it all.

Hope that helps.
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New post 13 May 2005, 22:43
THANK YOU, this really helps me understand this concept.
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New post 14 May 2005, 15:34
the way I always do these problems is by picking some arbitrary number that both rates can divide into.

For example, suppose the job = 12 units.

So every hour Sam completes 4 units of the job.

Every hour Mark completes 1 unit of the job.

Combine the rates = 5 units an hour.

12/5 = 2.4 or 2 and 2/5
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Re: Applied Arithmetic [#permalink]

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New post 19 May 2005, 07:00
above720 wrote:
Q:
If Sam can finish a job in 3 hours and Mark can finish a job in 12 hours, in how many hours could they finish the job if they worked on it together at their respective rates?

(A) 1
(B) 2 2/5
(C) 2 5/8
(D) 3 1/4
(E) 4

What may be different ways to solve this?


B

Time taken to complete the work together = 12*/15 = 2 2/5
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New post 19 May 2005, 23:03
The easiest way, if you ask me, is to say, in 12 hours Sam can get 4 jobs down and Mark can get 1 job down. So they get 5 jobs down in 12 hours. In other words they get 1 job done in 12/5 hours. Very straight forward.
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  [#permalink] 19 May 2005, 23:03
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