It takes an older pump 4 times as long to drain a certain pool as it does a newer pump. 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?

Let us say that:

x = the time it take for the new pump to drain the pool alone

4x = the time it take for the older pump

And we are given that together they drain the pool in 4 hours, therefore:

1/x + 1/4x = ¼

Multiply everything by x:

1 + ¼ = ¼ x

1.25 = 0.25 x

x = 5 hours

So, 4x = 20 hours

Hence it take the older pump 20 hours draining alone.