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?

4 hours

Step-by-step explanation:

Let h represent the number of hours the high-power pump requires to fill the pool. Then the number of pools it can fill per hour is 1/h. The low-power pump can fill 1/(h+2) pools in an hour. Together, they can fill 1 pool in 1.2 hours:

1/h + 1/(h+2) = 1/2.4

h+2 +h = h(h+2)/2.4 . . . . . . . multiply by h(h+2)

4.8h +4.8 = h^2 +2h . . . . . . multiply by 2.4

h^2 -2.8h = 4.8 . . . . . . . . . . put in form suitable for completing the square

h^2 -2.8h +1.96 = 6.76 . . . add (2.8/2)^2 = 1.96 to complete the square

h - 1.4 = √6.76 . . . . . . . . . . take the square root of both sides

h = 1.4 +2.6 = 4 . . . . . . . . . hours