Question

One water pipe fills a swimming bath in `x` hours. A second pipe takes `3` hours longer to fill the bath. The two pipes together fill the bath in two hours. How long will it take each pipe to fill the swimming bath separately?

Answer 1

I got `3 and 6` hours but check my maths anyway....

Explanation:

Have a look:

Answer 2

First pipe takes `3` hours to fill the pool and second pipe takes `6` hours to fill the pool.

Explanation:

First water pipe takes `x` hours to fill swimming bath

hence, in one hour, it fills `1/x` of the pool.

Second water pipe takes `x+3` hours to fill swimming bath

hence, in one hour, it fills `1/(x+3)` of the pool

In one hour they together fill `1/x+1/(x+3)=(2x+3)/(x^2+3x)`

as it should fill half of the pool, we have

`(2x+3)/(x^2+3x)=1/2`

or `x^2+3x=4x+6` i.e. `x^2-x-6=0`

i.e. `(x-3)(x+2)=0` and `x=3` or `-2`

As negative values are not permissible `x=3`

Hence first pipe takes `3` hours to fill the pool and second pipe takes `6` hours to fill the pool.