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

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

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New post 31 Mar 2019, 02:08
4
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

50% (01:57) correct 50% (02:09) wrong based on 46 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
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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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New post 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
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Re: A pump can fill a tank with water in 2 hours. Because of a  [#permalink]

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New post 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
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Re: A pump can fill a tank with water in 2 hours. Because of a  [#permalink]

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New post 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

Answer: D
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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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