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A uses 24 hours to pump out the water of a pool completely. [#permalink]
18 Jan 2005, 12:43

A uses 24 hours to pump out the water of a pool completely. B's rate is 2/3 that of A. If A worked for 8 hours at first and is then replaced by B, how many hours did B use to finish the work? _________________

"Forums are meant to benefit all. No one is interested in knowing what your guesses are. Please explain the reasoning behind the answer you chose. This will also help you organize your thoughts quickly during the exam."

A takes 24 hrs to finish 1 job...in 8 hrs it wud have finished 1/3 of the work...remainder of the 2/3 work has to be done by B. B takes 16 hrs to do 1 job so it wud take ite 16x2/3 to do 2/3 of the job.

Rate of B is 2/3 thjat of A. So B should need more time not less:) _________________

"Forums are meant to benefit all. No one is interested in knowing what your guesses are. Please explain the reasoning behind the answer you chose. This will also help you organize your thoughts quickly during the exam."

If There are X gallons pumped, then A's rate = 24 hrs for X gallons and B would be 36 hrs for X gallons

Hence, For 2/3 rd of the Job, B would need 12*2 = 24 hrs. _________________

"Forums are meant to benefit all. No one is interested in knowing what your guesses are. Please explain the reasoning behind the answer you chose. This will also help you organize your thoughts quickly during the exam."

A takes 24 hrs to finish 1 job...in 8 hrs it wud have finished 1/3 of the work...remainder of the 2/3 work has to be done by B. B takes 16 hrs to do 1 job so it wud take ite 16x2/3 to do 2/3 of the job.

Damn ! Big mistake, u r right...i took it as B takes 2/3 the time....in this case it is 36 * 2/3 = 24 hrs and not 16 * 2/3 = 32/3

A simple way to do Rate problems is to use the following formula:

X1/T1 + X2/T2 = J

X1= Time spent together by A
X2 = Time spent together by B
T1 = Time spent alone by A
T2 = Time spent alond by B
J= Fraction of job

Here, X1 =8, X2= unknown, T1=24, T2 = (3/2)*24 = 36, J= 1 (full job)
=> X2 = 24
(This problem could be solved in about 30 second with this method). This formula can be used for almost all rate problems, including the one that involves many people once you think through the problem and obtain the correct parameters to plug it into the above equation. In GMAT this will help in terms of time!

I think some of you misinterpreted the statement: B works at 2/3 the rate of A. This means, it takes B 3/2 as long as A to do the same job. Hence, if it takes A 24 h, it takes B 3/2 x 24h, i.e. 36 hours....

So A works at the rate of 1/24 h and B works at the rate of 1/36...Using these rates, u will arrive at the correct solution of 24.

B's rate is 2/3 of A means B can finish 2/3 of the amount that A can finish for the same period. A did 1/3 days work. B needs a day to finish 2/3 days of work. Therefore you get 24 easily without needing to calculate much.