One pump can fill a pool in 14 hours

Question

One pump can fill a pool in 14hr

. Working with a second slower pump, the pumps together can fill the pool in 10hr

. How fast can the second pump fill the pool by itself?

Answer 1

1/14 + 1/S = 1/10

in one hour one pump does 1/14 of filling the pool

in one hour the Slower pump fills 1/S of the pool

together they fill 1/10 of the pool in one hour

multiply by 70S

5S + 70 = 7S

2S = 70

S = 70/2 = 35 hours for the slower pump to fill the pool by itself

1/14 + 1/35 = 1/10

.07 +.03 = .10

in 1 hour one pump fills 7/100 of the pool

in 1 hour the slower pump fills 3/100 of the pool

together in one hour they fill (7+3)/100 = 1/10 of the pool