Question

Two pumps are filling a pool. One of them is high power and can fill the pool alone in 2 hours less time than the other can do so. Given that, working together, both pumps can fill the pool in 144 minutes, how long, in hours, will it take the powerful pump to fill the pool alone?

Answer 1

4 hours

Explanation:

Let x minutes be the time needed for the powerful pomp to fill the pool. Then x+120 minutes is the time needed to the other pomp to fill the pool. The powerful pomp fills
`(1)/(x)` of the pool in a minute and the other pomp fills
`(1)/(x+120)` of the pool in a minute. Filling together, they fill
`(1)/(x)+(1)/(x+120)` of the pool in a minute and

`144\cdot \left((1)/(x)+(1)/(x+120)\right)`

in 144 minutes.

Thus,

`144\cdot \left((1)/(x)+(1)/(x+120)\right)=1.`

Solve this equation:

`(144(x+120)+144x)/(x(x+120))=1,\\ \\144x+144\cdot 120+144x=x^2+120x,\\ \\x^2-168x-17280=0,\\ \\D=(-168)^2-4\cdot (-17280)=97344,\\ \\x_(1,2)=(-(-168)\pm √(97344))/(2)=(168\pm 312)/(2)=-72,\ 240.`

Hence, it is needed the powerful pomp 240 minutes = 4 hours to fill the pool.