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# A pump can fill a tank with water in 2 hours. Because of a

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Manager
Joined: 13 Aug 2018
Posts: 58
A pump can fill a tank with water in 2 hours. Because of a  [#permalink]

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31 Mar 2019, 02:08
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Difficulty:

75% (hard)

Question Stats:

48% (01:57) correct 52% (02:08) wrong based on 48 sessions

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A pump can fill a tank with water in 2 hours. Because of a leak, it took 2(1/3)
hours to fill the tank. The leak can drain all the water of the tank in ?

a. 7 hours
b. 10 hours
c. 12 hours
d. 14 hours
e. 4(2/3) hours

Posted from my mobile device
Intern
Joined: 18 Oct 2018
Posts: 16
Re: A pump can fill a tank with water in 2 hours. Because of a  [#permalink]

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02 Apr 2019, 11:58
2
jackfr2 wrote:
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2(1/3)
hours to fill the tank. The leak can drain all the water of the tank in ?

a. 7 hours
b. 10 hours
c. 12 hours
d. 14 hours
e. 4(2/3) hours

Posted from my mobile device

Let the draining rate be x.
It takes $$\frac{7}{3}$$ hours to fill the pool with the leak. The hourly rate with the leak is $$\frac{3}{7}$$.
The rate without the leak is $$\frac{1}{2}$$ --> $$\frac{1}{2} - x = \frac{3}{7}$$.
Solving this we get $$x = \frac{1}{14}$$ so it would take 14 hours for the leak alone to empty the tank. Answer: D
VP
Joined: 07 Dec 2014
Posts: 1227
Re: A pump can fill a tank with water in 2 hours. Because of a  [#permalink]

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02 Apr 2019, 17:58
1
jackfr2 wrote:
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2(1/3)
hours to fill the tank. The leak can drain all the water of the tank in ?

a. 7 hours
b. 10 hours
c. 12 hours
d. 14 hours
e. 4(2/3) hours

without leak, pump can fill 1 tank in 2 hours,
and thus could fill 7/6 of tank in 2 1/3 hours
but, with leak, 1/6 of tank instead drains in 2 1/3 hours
6*2 1/3=14 hours to drain entire tank
D
Target Test Prep Representative
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Posts: 9092
Location: United States (CA)
Re: A pump can fill a tank with water in 2 hours. Because of a  [#permalink]

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04 Apr 2019, 18:19
jackfr2 wrote:
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2(1/3)
hours to fill the tank. The leak can drain all the water of the tank in ?

a. 7 hours
b. 10 hours
c. 12 hours
d. 14 hours
e. 4(2/3) hours

Posted from my mobile device

The pump’s rate is 1/2 to fill the tank. We can let x = the number of hours the leak can drain all the water in the tank, and so its rate is 1/x. We can create the equation:

1/2 - 1/x = 1/(7/3)

1/2 - 1/x = 3/7

Multiplying by 14x, we have:

7x - 14 = 6x

x = 14

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Re: A pump can fill a tank with water in 2 hours. Because of a   [#permalink] 04 Apr 2019, 18:19
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