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 Post subject: GMAT RatePosted: Sat Dec 18, 2010 12:26 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

(E) If Angela, Bernie, and Colleen can complete a job in 4 hours, they can complete 1/4 of the job in an hour. Furthermore, if Angela and Bernie can complete the same job in 5 hours, they can do 1/5 of the entire job in an hour.

If the three of them can do 1/4 of a job in an hour, and without Colleen the other two can do 1/5 of a job in an hour, then the amount of the job Colleen can do in an hour is the difference of these results:
1/4 – 1/5 = 5/20 – 4/20 = 1/20.

Since Colleen can do 1/20 of the job in an hour, it will take her 20 hours to do the entire job by herself.

The correct answer is choice (E).
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Where are you getting the 1/4 and 1/5? Im not following.

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 Post subject: Re: GMAT RatePosted: Sat Dec 18, 2010 12:36 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Let's denote the rates of Angela, Bernie, and Colleen by a, b, c respectively. All rates are denoted in job per. hour.

Then "Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours." means:
(a + b + c) × 4 = 1
a + b + c = 1/4

"Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours."
(a + b) × 5 = 1
a + b = 1/5

If we plug the second one into the first one, we get:
1/5 + c = 1/4
c = 1/20

The rate of Coleen is 1/20 of a job per hour. Therefore 1/20 × t = 1, where t is the time it takes Coleen to complete the job.
t = 20

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