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

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kapsycumm
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Working together, 7 identical pumps can empty a pool in 6 [#permalink] New post   Updated on: 18 Oct 2012, 05:10
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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
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E

Originally posted by kapsycumm on 17 Oct 2012, 21:32.
Last edited by Bunuel on 18 Oct 2012, 05:10, edited 1 time in total.
Renamed the topic.
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KarishmaB
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Re: Pumps emptying water [#permalink] New post   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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azzhhuu
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Re: Pumps emptying water [#permalink] New post   17 Oct 2012, 21:41
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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, 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] New post   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] New post   14 Nov 2012, 05:48
\(\frac{7}{p}=\frac{1}{6}==>Rpump=\frac{1}{42}\)

Calculate time for 4 pumps to fill pool:

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

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


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] New post   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.

Answer: E
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Re: Working together, 7 identical pumps can empty a pool in 6 [#permalink] New post   16 Aug 2018, 03:57
Could Some one explain to me this question with the rate*time=work equation pleas. Bunuel chetan2u, I would appreciate your help on this if you can. Thanks!
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Re: Working together, 7 identical pumps can empty a pool in 6 [#permalink] New post   16 Aug 2018, 04:03
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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


Say rate of work of one pump is R.

Work = Rate*Time = 7R * 6 = 42R

The work is the same if we use 4 pumps but the are decreases to 4R

42R = 4R *Time
Time = 42/4 = 10.5 hrs
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Re: Working together, 7 identical pumps can empty a pool in 6 [#permalink] New post   16 Aug 2018, 04:38
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venky964 wrote:
Could Some one explain to me this question with the rate*time=work equation pleas. Bunuel chetan2u, I would appreciate your help on this if you can. Thanks!


Hi Venky,
As also explained by Karishma, total work required = rate*time= 7pumps*6hour=42 pump hours
So if 4 pumps are working together ..
W=rate *time..... So 42 pump hours=4pumps*time....
Time =42/4=10.5 hours
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Re: Working together, 7 identical pumps can empty a pool in 6 [#permalink] New post   16 Aug 2018, 04:49
Thanks a lot for your explaination. Just could not recognize that the 7 pumps here is the rate. now it is clear.

Thanks once again chetan2u
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Re: Working together, 7 identical pumps can empty a pool in 6 [#permalink] New post   28 Jan 2022, 17:36
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