Two pipes can be used

Question

Two pipes can be used to fill a pool. Working together, the two pipes can fill the pool in two hours. The larger pipe can fill the pool in three hours less time than the smaller pipe can alone. Find the time to the nearest 10th of an hour it takes for the smaller pipe working alone to fill the pool.

Answer 1

The combined work rate is 1/2

the smaller pipe has work rate x hours to fill the pool ---> the workrate is 1/x

the larger pipe is 3 hours faster, so it takes x-3 hours ---> the work rate is 1/(x-3)

1/x + 1/(x-3) = 1/2

2(x-3) + 2x = x(x-3)

2x - 6 + 2x = x^2 - 3x

4x - 6 = x^2 - 3x

0 = x^2 - 7x + 6

0 = (x-6)(x-1)

x = 1 or x = 6

x=1 results in negative times

the smaller pipe takes 6 hours to fill the pool --> work rate is 1/6 pool per hour

the larger pipe takes 3 hours to fill the pool --> work rate is 1/3 pool per hour

working together ---> 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2