Question

Drains A and B are used to empty a swimming pool. Drain A alone can empty the pool in 4.75 hours. How long will it take drain B alone to empty the pool if it takes 2.6 hours when both drains are turned on?

Answer 1

B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and it takes 2.6 hours when both drains are turned on.

Explanation:

The given is,

A alone can empty the pool in 4.75 hours.

It takes 2.6 hours when both drains are turned on.

Step:1

One hour work drains A and B =

One hour work of drain A + One hour work of Drain B.........(1)

One hour work of Drain A =
`(1)/(4.75)`

One hour of ( A + B ) =
`(1)/(2.6)`

Equation (1) becomes,

One hour work of B = One hour work of ( A + B )

- One hour work of A

Substitute the values,

One hour work of B =
`(1)/(2.6) - (1)/(4.75)`

=
`(4.75-2.6)/((4.75)(2.6))`

=
`(2.15)/(12.35)`

=
`(1)/(5.744)`

One hour work of B =
`(1)/(5.744)`

B alone can empty the pool in 5.744 hours

Result:

B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and it takes 2.6 hours when both drains are turned on.