Question

A new type of pump can drain a certain pool in 9 hours. An older pump can drain the pool in 11 hours. How long will ittake both pumps working together to drain the pool?

Answer 1

Given:

A new type of pump can drain a certain pool in 9 hours.

An older pump can drain the pool in 11 hours.

To find:

The required time when both pumps work together to drain the pool.

Step-by-step explanation:

One hour's work of the new pipe is,

`(1)/(9)`

One hour's work of the old pipe is,

`(1)/(11)`

So, one hour's work of both the pipe together is,

`\begin{gathered} (1)/(9)+(1)/(11)=(11+9)/(9(11)) \\ =(20)/(99) \end{gathered}`

Therefore, the time taken to drain the pool for both the pipes together is,

`\begin{gathered} (99)/(20)hours \\ (or) \\ 4\text{ }hours\text{ 57minutes} \end{gathered}`

Final answer:

The required time to drain the pool for both the pipes together is 4 hours 57 minutes.