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

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Intern
Joined: 08 Oct 2012
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Working together, 7 identical pumps can empty a pool in 6 [#permalink]

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17 Oct 2012, 21:32
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81% (00:56) correct 19% (02:01) wrong based on 141 sessions

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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, 05:10, edited 1 time in total.
Renamed the topic.

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17 Oct 2012, 22:21
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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: Working together, 7 identical pumps can empty a pool in 6 [#permalink]

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22 Mar 2017, 09:46
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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

We are given that the rate of 7 pumps is 1/6. We can use a proportion to determine the rate of 4 pumps in which x is the rate of the 4 pumps.

7/(1/6) = 4/x

42 = 4/x

42x = 4

x = 4/42 = 2/21

Since the rate of the 4 pumps is 2/21, the time needed for them to empty the pool is 1/(2/21) = 21/2 = 10.5 hours.

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Intern
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17 Oct 2012, 21:41

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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18 Oct 2012, 02:53
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]

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18 Oct 2012, 08:41
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]

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14 Nov 2012, 05:48
$$\frac{7}{p}=\frac{1}{6}==>Rpump=\frac{1}{42}$$

Calculate time for 4 pumps to fill pool:

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

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Re: Working together, 7 identical pumps can empty a pool in 6 [#permalink]

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19 Mar 2017, 03:35
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Re: Working together, 7 identical pumps can empty a pool in 6 [#permalink]

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20 Mar 2017, 04:08
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

let the flow be x L/hr and t be the . According to the question

7*x*6 = 4*x*t
or t = 21/2 or 10 +1/2

option E

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Re: Working together, 7 identical pumps can empty a pool in 6   [#permalink] 20 Mar 2017, 04:08
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