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by ramonsa » Wed Jun 03, 2009 3:50 pm
15. Working alone, R can complete a certain kind of job in 9 hours. R and S, working together at their respective rates, can complete one of these jobs in 6 hours. In how many hours can S, working alone, complete one of these jobs?
(A) 18 (B) 12 (C) 9
(D) 6 (E) 3
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by syr » Wed Jun 03, 2009 5:28 pm
First of all, this should be posted in the Problem Solving (PS) section of the GMAT. This is the Data Sufficiency (DS) section

Here is the explanation --

Given, R can complete the job in 9hrs.
Therefore, in 1 hr he can complete 1/9th of the job. This is basically his rate.

R -> 1/9 th of work in 1 hr

Given, R + S can complete the same job in 6hrs.
Therefore, in 1hr they can complete 1/6th of the job. This is the rate for both R and S working together.

So, if we find the rate at which S works, we can determine the number of hrs he requires for the job.

Rate of S = Rate of (R + S) - Rate of R
= 1/6 - 1/9
= 1/18

Thus S's rate is 1/18. ie he can complete 1/18 of work in 1 hr
Thus, he will take 18 hrs to complete the whole job.

Answer is A)18

HTH
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by anoop.dimri » Wed Feb 06, 2013 11:45 am
R*9=(R+S)*6
R=2S
Work done by R is performed in such hours, and S requires double (2) time to complete the same work
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by Brent@GMATPrepNow » Wed Feb 06, 2013 11:56 am
ramonsa wrote:15. Working alone, R can complete a certain kind of job in 9 hours. R and S, working together at their respective rates, can complete one of these jobs in 6 hours. In how many hours can S, working alone, complete one of these jobs?
(A) 18
(B) 12
(C) 9
(D) 6
(E) 3
Let's assign a "nice" value to the job.
Say, the job is to make 18 widgets (since 9 and 6 both divide nicely into 18).

R can complete the job in 9 hours
In other words, R can make 18 widgets in 9 hours.
This means that machine R's rate is 2 widgets/hour

Together, R and S can complete the job in 6 hours
In other words, R+S can make 18 widgets in 6 hours.
This means their combined rate is 3 widgets/hour

So, working along, Machine S's rate must be 1 widget/hour.

In how many hours can S, working alone, complete one of these jobs?
So, machine S must make 18 widgets, and its rate is 1 widget/hour.
So, it will take 18 hours

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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