It takes an older pump 4 times as long to drain a certain po

It takes an older pump 4 times as long to drain a certain pool as it does a newer pumps. Working together, it takes the two pumps 4 hours to drain the pool. How long will it take the older pump to drain the pool working alone?

Solution

Let older pump take x hrs to fill pond

In 1 hr it takes 1/xth of the pool

new pump would take x/4 hrs

In 1 hr would take 4/x th of the pool

Together, (1/x +4/x ) = 1/4

1/x( 5/4) = 1/4

1/x(5/1) =1

x =5 hrs