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Three identical pumps, pumping at the same constant rate, can remove a

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Three identical pumps, pumping at the same constant rate, can remove a  [#permalink]

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New post 06 Oct 2019, 21:19
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EMPOWERgmat PS Series:
Pack 2, Question 4

Three identical pumps, pumping at the same constant rate, can remove a total of 1,250 gallons of water from a tank in 1 hour. With X of these pumps, 15,000 gallons of water could be removed in 3 hours. What is the value of X?

A. 9
B. 12
C. 15
D. 18
E. 21



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Re: Three identical pumps, pumping at the same constant rate, can remove a  [#permalink]

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New post 07 Oct 2019, 01:02
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EMPOWERgmatRichC wrote:
Three identical pumps, pumping at the same constant rate, can remove a total of 1,250 gallons of water from a tank in 1 hour. With X of these pumps, 15,000 gallons of water could be removed in 3 hours. What is the value of X?

A. 9
B. 12
C. 15
D. 18
E. 21


3 pumps in 1 hour remove 1250 gallons
3 pumps in 3 hour remove 1250*3 gallons
So, 1 pump in 3 hour will remove \(\frac{1250*3}{3}\) or 1250 gallons

Now, 1250 gallons can be removed in 3 hrs by 1 pump..
so 1 gallon can be removed in 3 hrs by \(\frac{1}{1250}\) pump..
Thus, 15,000 gallons can be removed in 3 hrs by \(\frac{15,000}{1250}\) or 12 pumps..
So, \(X=12\)

B
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Re: Three identical pumps, pumping at the same constant rate, can remove a  [#permalink]

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New post 10 Oct 2019, 21:34
OFFICIAL EXPLANATION

Hi All,

We're told that 3 identical pumps, pumping at the same constant rate, can remove a total of 1,250 gallons of water from a tank in 1 hour. With X of these pumps, 15,000 gallons of water could be removed in 3 hours. We're asked for the value of X.

The information in this prompt is ratio-based (1 hour vs. 3 hours; 1,250 gallons vs. 15,000 gallons), so there are a number of different calculations that you can do to solve it. If you do not immediately see how to set up a ratio, then you can still get to the correct answer: you might not immediately recognize that 15,000 is a multiple of 1,250 - but with just a little work, you can prove it.

3 pumps --> 1,250 gallons removed in 1 hour
6 pumps --> 2,500 gallons removed in 1 hour
12 pumps --> 5,000 gallons removed in 1 hour

At this point, you might recognize that 5,000 divides into 15,000....

36 pumps --> 15,000 gallons removed in 1 hour

At this point, we know that we'll need 36 pump-hours worth of work to remove 15,000 gallons of water. Since we want to remove that water over the course of 3 hours, we just have to divide this number by 3 --> 36/3 = 12 machines.

Final Answer:

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Re: Three identical pumps, pumping at the same constant rate, can remove a  [#permalink]

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New post 29 Nov 2019, 18:57
Quote:
Three identical pumps, pumping at the same constant rate, can remove a total of 1,250 gallons of water from a tank in 1 hour. With X of these pumps, 15,000 gallons of water could be removed in 3 hours. What is the value of X?

A. 9
B. 12
C. 15
D. 18
E. 21


3 pumps = 1250 gallons = 1 hours

15000 gallons in 3 hours.
5000 in one hour.
I know 1250 can be done by 3 pumps.
5000 will need 3*4=12 pumps.

Option B
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Re: Three identical pumps, pumping at the same constant rate, can remove a   [#permalink] 29 Nov 2019, 18:57
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