A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 9:00 am and some time later the drain that empties the pool was also opened. If the pool was filled by 9:00 pm and not earlier, when was the drain opened? Select the correct option.
A) at 10:00 am  B) at 11:00 am  C) at 12:00 pm  D) at 1:00 pm  E) at 2:00 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 + (12-x)/20 = 1   5x + 12 - x = 20   4x = 8   x = 2   The answer is 11:00 am.   The answer is at 11:00 am.
<result>B</result>
A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 9:00 am and some time later the drain that empties the pool was also opened. If the pool was filled by 9:00 pm and not earlier, when was the drain opened?