A pool has two inlet pipes. The first inlet can fill the pool in 6 hours, the other can fill it in 4 hours. If the first pipe is open for 2 hours and then the second is open. How long will take for the pool to be filled after the second pipe is open?
1) First pipe open for 2 hours, thus 2 hours / 6 hours = 1/3 of the pool is filled.
Whole pool = 3/3 - 1/3 already filled = 2/3 left to be filled.
2. Second pipe is opened. Two pipes working together = 1/6 + 1/4. Common denominator = 4/24 + 6/24 = 10/24.
Factoring down 10/24, result is 5/12. This is now the rate of the two pipes working together.
To complete, take amount of pool left to be filled (2/3) divided by the rate (5/12).
(2/3) / (5/12) translates into (2/3) x (12/5) = 24/15, or 8/5.
Question asks how long it take to fill the rest of the pool after the second pipe is opened.
Answer is 1 3/5, or 1.6 hours.