One pump can fill a pool in ten minutes another can fill the pool in 15 minutes how long to fill the pool if both pumps are running?

The first pump fills (1/10th) of the pool in 1 minute.

The second pump fills (1/15th) of the pool in 1 minute.

With both running, they fill

(1/10 + 1/15) = (3/30 + 2/30) = 5/30 = 1/6th of the pool in 1 minute.

They have to run for [ 1 / (1/6) ]

= 6 minutes in order to fill the pool.