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

New pump = (Old Pump * Total) / (Old Pump - Total)
New pump = (14 * 6) / (14 -6)
New pump = (84) / (8)
New Pump = 10.5 hours

Answer 2

10.5 hours.

Explanation:

Given,

Two pumps can drain a certain pool in 6 hours.

So, the combined one hour work of the pumps =
`(1)/(6)`,

Also,older pump takes 14 hours to drain the pool by itself,

The one hour work of older pump =
`(1)/(14)`,

Thus, the one hour work of newer pump = Combined one hour work - one hour work of older pump,

`=(1)/(6)-(1)/(14)`

`=(7-3)/(42)`

`=(4)/(42)`

Hence, the total time taken by newer pump =
`(1)/(4/42)=(42)/(4)=10.5\text{ hours}`