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Working together, 7 identical pumps can empty a pool in 6

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Working together, 7 identical pumps can empty a pool in 6 [#permalink] New post 17 Oct 2012, 20:32
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A
B
C
D
E

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86% (01:47) correct 14% (02:43) wrong based on 51 sessions
Working together, 7 identical pumps can empty a pool in 6 hours. How many hours will it take 4 pumps to empty the same pool?

A. 4 2/3
B. 9 1/4
C. 9 1/3
D. 9 3/4
E. 10 1/2
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Oct 2012, 04:10, edited 1 time in total.
Renamed the topic.
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Re: Pumps emptying water [#permalink] New post 17 Oct 2012, 21:21
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kapsycumm wrote:
Working together, 7 identical pumps can empty a pool in 6 hours. How many hours will it take 4 pumps to empty the same pool?

A. 4 2/3
B.9 1/4
C. 9 1/3
D. 9 3/4
E. 10 1/2


7 pumps working for 6 hrs complete one work i.e. you need 7*6 = 42 pump-hours to finish that work. This means that 1 pump will take 42 hrs to complete the work or 42 pumps will take 1 hr to complete the work.

Now, you can have quickly calculate no of hrs required for any number of pumps or number of pumps required for any given number of hrs.

Given 4 pumps, it will take 42/4 = 10.5 hrs to finish the work

Given 8 pumps, it will take 42/8 = 5.25 hrs to finish the work

Given that you need to complete the work in 7 hrs, you need 42/7 = 6 pumps for it.

Given that you need to complete the work in 3 hrs, you need 42/3 = 14 pumps for it.
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Re: Pumps emptying water [#permalink] New post 17 Oct 2012, 20:41
The answer is E

7 pumps take 6 hours. 1 Pump will take 6*7 hours . Hence 4 pumps will take (6*7)/4 = 21/2 = 10 1/2 hours
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Re: Pumps emptying water [#permalink] New post 18 Oct 2012, 01:53
I'll just assume the volume of the pool is 42 litres. So each pump's capacity is 1 litre/hour. 4 pumps = 4 litres per hour. So 42/4 = 10.5
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Re: Working together, 7 identical pumps can empty a pool in 6 [#permalink] New post 18 Oct 2012, 07:41
Thanks guys. I was little confused with this, but now it is clear.
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Re: Working together, 7 identical pumps can empty a pool in 6 [#permalink] New post 14 Nov 2012, 04:48
\frac{7}{p}=\frac{1}{6}==>Rpump=\frac{1}{42}

Calculate time for 4 pumps to fill pool:

\frac{4}{42t}=1 ==> t=\frac{21}{2}=10\frac{1}{2}hours

Answer:E
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Re: Working together, 7 identical pumps can empty a pool in 6   [#permalink] 14 Nov 2012, 04:48
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