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Working at a constant rate, Sam can finish a job in 3 hours. Mark, also working at a constant rate, can finish the same

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by BTGmoderatorDC » Wed Jun 03, 2020 6:57 pm

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Difficulty—

Working at a constant rate, Sam can finish a job in 3 hours. Mark, also working at a constant rate, can finish the same job in 12 hours. If they work together for 2 hours, how many minutes will it take Sam to finish the job, working alone at his constant rate?

A. 5
B. 20
C. 30
D. 60
E. 120


OA C

Source: Princeton Review
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Re: Working at a constant rate, Sam can finish a job in 3 hours. Mark, also working at a constant rate, can finish the s

by Jay@ManhattanReview » Wed Jun 03, 2020 10:46 pm
BTGmoderatorDC wrote: ↑
Wed Jun 03, 2020 6:57 pm
 Working at a constant rate, Sam can finish a job in 3 hours. Mark, also working at a constant rate, can finish the same job in 12 hours. If they work together for 2 hours, how many minutes will it take Sam to finish the job, working alone at his constant rate?

A. 5
B. 20
C. 30
D. 60
E. 120

OA C

Source: Princeton Review
Given the information, Sam can work 1/3 part of the work in 1 hour or 2/3 part of the work in 2 hours; similarly, Mark can work 1/12 part of the work in 1 hour or 2/12 = 1/6 part of the work in 2 hours.

Thus, in 2 hours they together finish 2/3 + 1/6 = 5/6 part of the work.

Thus, the work left to be done = 1 – 5/6 = 1/6

Since San can do 1/3 part of the work in 1 work, he can do 1/6 part of the work in 1/2 hour or 30 min.

The correct answer: C

Hope this helps!

-Jay
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Re: Working at a constant rate, Sam can finish a job in 3 hours. Mark, also working at a constant rate, can finish the s

by Scott@TargetTestPrep » Sat Apr 03, 2021 10:30 am
BTGmoderatorDC wrote: ↑
Wed Jun 03, 2020 6:57 pm
 Working at a constant rate, Sam can finish a job in 3 hours. Mark, also working at a constant rate, can finish the same job in 12 hours. If they work together for 2 hours, how many minutes will it take Sam to finish the job, working alone at his constant rate?

A. 5
B. 20
C. 30
D. 60
E. 120


OA C

Solution:

The rate of Sam is 1/3 and the rate of Mark is 1/12. We can let Sam’s time = 2 + x hours and Mark’s time = 2 hours; thus:

(1/3)(2 + x) + (1/12)(2) = 1

(2 + x)/3 + 1/6 = 1

Multiplying the equation by 6, we have:

4 + 2x + 1 = 6

2x = 1

x = 1/2 hour = 30 minutes

Answer: C

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