Question

A hose can fill a swimming pool in 3 hours. Another hose needs 4 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool?

Answer 1

A hose can a swimming pool in 3 hours.

So it fills the pool 1/3 per hour

Let the time taken by the second hose to fill the pool be x

So it feel the pool 1/x per hour

When combined they fill the pool at

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

So the time taken to fill the pool when used together is

`(3x)/(x+3)`

The time the second hose takes is x is 4 more hours then the two hose combined

It follows

`x-4=(3x)/(x+3)`

Solve the equation for x

`\begin{gathered} x^2+3x-4x-12=3x \\ x^2-4x-12=0 \\ x^2-6x+2x-12=0 \\ x(x-6)+2(x-6)=0 \\ (x-6)(x+2)=0 \\ x=6,x=-2 \end{gathered}`

Hence the time taken by the two hose is

`(3*6)/(3+6)=(18)/(9)=3`

Therefore it will take 3 hours for the hose to fill the pool together.