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# A uses 24 hours to pump out the water of a pool completely.

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Senior Manager
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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?
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VP
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32/3 ==> 10.6 hrs

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.
Senior Manager
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Rate of B is 2/3 thjat of A. So B should need more time not less:)
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Intern
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The first Pump has done 1/3 of the work, 8 hours/ 24 hours for the whole pump = 1/3 the pool.

The second pump can remove 1/16 of the pool every hour, there is 2/3 of the pool remaining, 2/3 * 16 hours = 10 2/3 hours

if you say that B's time is 2/3 of A's time would this not mean that
2/3 * 24 hours is 16 hours.

or the answer is 8 hours * 3/2 = 12 hours for pump B
Senior Manager
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Post is not vague:

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.
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VP
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banerjeea_98 wrote:
32/3 ==> 10.6 hrs

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
Senior Manager
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A takes 24 hours to do 1 job therefore his rate = 1/24 job/hr

B's rate is 2/3 of A's so therefore his rate = 2/3 x 1/24 = 1/36 job/hr

A works for 8 hours so he completes 8 x 1/24 = 8/24 of job

Therefore there is 16/24 of the job still remaining so you divide that by B's rate

= (16/24 job)/(1/36 job/hr) = 24hrs for B to complete the rest of the job.
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Director
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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!
Director
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A takes 24 hrs so in 8 hrs 1/3 d job done

B will finish 2/3 jon in 2 /3*16 = 10.6 hrs
Intern
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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.

Thanks,
F.
SVP
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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.
VP
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A worked for 8 Hours. the remaining hours of work out of 24 are 16.
rate of B is 2/3 of A.
B can work the 16 hours of work in 16*3/2=24 hours........
Manager
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24 [#permalink]  07 Feb 2005, 14:06
B can do in 3/2*24 = 36 hrs.
In 8 hrs by a 1/3 of work is done so 2/3 is left.

Time taken by B = 2/3*36 = 24 hrs.
VP
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A => 24

B => 3/2 of 24 => 36

8/24 + x/36 = 1

solve for x

x = > 12
Intern
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A does it in 24 hours
B does it in 36 hours

there is 2/3 of the job left, so 2/3 * 36 - 24
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