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 11:00 pm and not earlier, when was the drain opened?
Choose the correct answer: A) at 10:30 am B) at 11:30 am C) at 12:30 pm D) at 1:30 pm E) at 2:30 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 + (14-x)/20 = 1   5x + 14 - x = 20   4x = 6   x = 1.5   The answer is 10:30 am.   The answer is at 10:30 am.
<result>A</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 11:00 pm and not earlier, when was the drain opened?