An inlet pipe can fill an empty pool in 5 hrs, another inlet pipe can fill the pool in 4 hours. How long will it take both pipes to fill the pool?

Question

solve and verify your answer

Answer 1

The simple way to do this type of problem is to take the reciprocal of each, add them together, and then take the reciprocal of that number.

 

1/5 + 1/4 =

4/20 + 5/20 = 9/20

20/9 = 2 and 2/9 hours (2 hours, 13 minutes and 20 seconds)

 

To understand why this works, realize that the first pipe fills 1/5 of the pool in an hour, and the second pipe fills 1/4 of the pool in an hour.  So together they fill 9/20 (1/5 + 1/4) of the pool in an hour.  To find the total time we take 1 pool and divide it by 9/20 to get 20/9 hours.