SOLUTION
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
[tex]\frac{1}{3}+\frac{1}{x}=\frac{x+3}{3x}[/tex]
So the time taken to fill the pool when used together is
[tex]\frac{3x}{x+3}[/tex]
The time the second hose takes is x is 4 more hours then the two hose combined
It follows
[tex]x-4=\frac{3x}{x+3}[/tex]
Solve the equation for x
[tex]\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}[/tex]
Hence the time taken by the two hose is
[tex]\frac{3\times6}{3+6}=\frac{18}{9}=3[/tex]
Therefore it will take 3 hours for the hose to fill the pool together.
