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

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

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?