Problem Solving

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?

at 2:00 pm
at 2:30 pm
at 3:00 pm
at 3:30 pm
at 4:00 pm

OA - D

crackgmat007 wrote: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?

at 2:00 pm
at 2:30 pm
at 3:00 pm
at 3:30 pm
at 4:00 pm

OA - D

Hi crackgmat007,

The valve that fills the pool pumps water into the pool at a rate of 1/4 pool per hour. The valve that drains the pool drains it at a rate of 1/5 pool per hour. When both valves are on, the rate at which the pool fills will be the difference between these two rates: 1/4 - 1/5 = 1/20 pool per hour.

We know that the pool was filled in ten hours, and that the "pump-in" valve was on for some time before the drain valve got turned on. The time that only the pump-in valve was on, we can call "x".

So, for x hours the pool was being filled up at a rate of 1/4 pool per hour. And then, for 10-x hours, the pool was being filled up at a rate of 1/20 pool per hour. And in ten hours, exactly one pool got filled:

x/4 + (10-x)/20 = 1 pool
x = 2.5 hours

So the pump-in valve was on for 2.5 hours by itself.

Choose D.

Note that backsolving, using the answer choices with a little bit of algebra would likely have been more efficient than pure algebra.

amazing explanation. thanks