Working alone, R can complete a certain kind of job in 9 hours. R and S,

[BTGModeratorVI]

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

Source: Official Guide
Answer: A

[Jay@ManhattanReview]

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

Source: Official Guide
Answer: A

Part of the job done by R and S, working together in an hour = 1/6 (given);
Part of the job done by R, working alone in an hour = 1/9 (given);

Thus, Part of the job done by S, working alone in an hour = 1/6 – 1/9 = 1/18;

Thus, S, working alone can complete the job in 1/(1/18) = 18 hours

The correct answer: A

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

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

Source: Official Guide
Answer: A

One approach is to assign a "nice" value to the entire job.
So let's use a number that works well with the two given values of 9 hours and 6 hours.
Let's say the job consists of making 54 widgets.

Working alone, R can complete a certain kind of job in 9 hours.
In other words, R can make 54 widgets in 9 hours.
This means R's RATE = 6 widgets per hour

R and S, working together at their respective rates, can complete one of these jobs in 6 hours
In other words, R and S can make 54 widgets in 6 hours.
This means their COMBINED rate = 9 widgets per hour

9 - 6 = 3
So, S's RATE = 3 widgets per hour

In how many hours can S, working alone, complete one of these jobs?
Another words, how much time will it take S to make 54 widgets?

Time = output/rate
So, time = 54/3 = 18 hours

Answer: A

Cheers,
Brent