Question

A small pump can drain a pool in 9 hours. A large pump could drain the same pool in 3 hours. How long​ (to the nearest​ minute) will it take to drain the pool if both pumps are used​ simultaneously?

Answer 1

Answer: 22.5 hours

Explanation:

Let t be the time taken by both of the pumps to drain the pool.

Given: Time taken by pump 1 to drain the pool alone= 9 hours.

Time taken by pump 2 to drain the pool alone= 3 hours.

If both pumps are used​ simultaneously, then

`\frac1t=\frac19+\frac13\\\\\Rightarrow\ \frac1t=(1+3)/(9)\\\\\Rightarrow\ \frac1t=\frac49\\\\\Rightarrow\ t=\frac94\\\\\Rightarrow\ t=2.25`

Hence, it will take 22.5 hours to drain the pool if both pumps are used​ simultaneously.