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m20 q32

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m20 q32 [#permalink] New post 04 Jul 2010, 05:47
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A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain 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

[Reveal] Spoiler:
When only the valve is open, the pool is filling at a rate of \frac{1}{4} an hour. When both the valve and the drain are open, the pool is filling at a rate of \frac{1}{4} - \frac{1}{5}= \frac{1}{20} an hour. Let x denote the time when only the valve was open. Then both the valve and the drain were open for 11-1-x = 10-x hours. Now we can compose the equation \frac{1}{4}x+\frac{1}{20}(10-x)=1 which reduces to \frac{x}{5}=0.5 from where x=2.5 . Thus, the drain was opened at 1:00 + 2:30 = 3:30 pm.

The correct answer is D.


Can someone please explain/ simplify the wording of the problem for me please?
The explanation provided is straightforward enough, but I could not set the correct equation up because I could get my head round the 3rd statement :oops:
Does the pool fill at 11pm the following day, or was it full at 11pm the previous day?
To derive the solution, does it even matter if the pool was full the previous day or the it filled up the following day?
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Re: m20 q32 [#permalink] New post 04 Jul 2010, 14:14
Hi,

You have to assume that the pool was empty. Otherwise you cannot solve the problem.

The valve that fills the pool was opened at 1:00 pm in the afternoon just at my lunch time :).

If the pool was filled by 11:00 pm and not earlier, when was the drain opened? Here 11:00pm is 10 hours after my lunch time :) and ie 1 hour just before midnight.

I hope I got your questions right and answered them accordingly.

regards,
Jack
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Re: m20 q32 [#permalink] New post 04 Jul 2010, 21:50
suddenly it all makes sense
thanks a lot jakolik!
Re: m20 q32   [#permalink] 04 Jul 2010, 21:50
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