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 7:00 pm and not earlier, when was the drain opened?  Choose one:
A) at 2:00 pm  B) at 2:30 pm  C) at 3:00 pm  D) at 3:45 pm  E) at 4:30 pm
The filling rate is 1/4 and the draining rate is 1/5.   The combined rate of filling and draining is 1/4 - 1/5 = 1/20.   Let x be the number of hours before the drain was opened.   x/4 + (6-x)/20 = 1   5x + 6 - x = 20   4x = 14   x = 3.5   The answer is 4:30 pm.   The answer is at 4:30 pm.
<result>E</result>
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 7:00 pm and not earlier, when was the drain opened?