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M20-32

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Bunuel
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M20-32 [#permalink] New post   16 Sep 2014, 01:09
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66% (02:30) correct 34% (02:34) wrong based on 282 sessions
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A filling pipe can fill an empty swimming pool in 4 hours, while a drain valve can empty the full pool in 5 hours. To fill the empty pool, the filling pipe was opened at 1:00 pm, and after some time, a drain valve was also opened. If the pool was filled at 11:00 pm, when was the drain valve opened?

A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm
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Bunuel
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Re M20-32 [#permalink] New post   16 Sep 2014, 01:09
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A filling pipe can fill an empty swimming pool in 4 hours, while a drain valve can empty the full pool in 5 hours. To fill the empty pool, the filling pipe was opened at 1:00 pm, and after some time, a drain valve was also opened. If the pool was filled at 11:00 pm, when was the drain valve opened?

A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm


The rate of the filling pipe is given as \(\frac{1}{4}\) pool/hour and the rate of drain valve is given as \(\frac{1}{5}\) pool/hour. The filling pipe was opened for 10 hours, from 1:00 pm to 11:00 pm. Let x denote the time for which the drain valve was opened, then we'd have \(10*\frac{1}{4} - x*\frac{1}{5} = 1\), which gives \(x = 7.5\) hours. Hence, the drain valve was opened for 7.5 hours, and therefore was opened at 11:00 pm - 7.5 hours = 3:30 pm.


Answer: D
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Bunuel
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Re: M20-32 [#permalink] New post   03 Jul 2023, 14:54
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M20-32 [#permalink] New post   05 Dec 2023, 20:07
I solved it this way:

First identify that it was emptied for 10 hours. From 13:00 to 23:00 hrs.

Second multiply the emptying ratio (1/4)*10 hrs. Resulting in 10/4 or 5/2. Corresponding to the emptying of 2 and a half pools.

Third, I subtract the envelope of the emptying of one pool from step two. 5/2-2/2 = 3/2.

Fourth, the 3/2 corresponds to the filling ratio by the number of hours "x" that it was on. 3/2 = (1/5)* x ---> 7,5 = X

Fifth, I subtract from 23:00 hrs the 7.5 hours that the filling was on. Result 15:30.
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Re: M20-32 [#permalink] New post   21 Mar 2024, 14:12
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­when both the tap and valve are open, filling rate = 1/4- 1/5 = 1/20.  In 20 hours, entire tank will be filled, in 10 hours only 1/2 the tank will be filled. Since the tank was filled in 10 hours, the tap must have been opened to fill more than 1/2 the tank. So answer must be more than 2 hours.  A, B & C are out. in 2.5 hours, 2.5/4 or 5/8th filled and remaining 3/8th can be done in (3/8)*20= 15/2=7.5 hours. 7.5+2.5 =10.  
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Re: M20-32 [#permalink]
21 Mar 2024, 14:12
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