Question

Working together, two pumps can drain a certain pool in 6 hours. If it takes the older pump 14 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?

Answer 1

in 6 hrs, the old pump drains 6/14 of the pool
... so the newer pump drains 8/14 in 6 hr

(8/14) / 6 = 1 / x ... x = 6 / (8/14)

Answer 2

adding up the amount each pump can do in an hour, we have
1/14 + 1/x = 1/6