Question

A swimming pool is filled with three pipes with uniform flow. The first two pipes operating simultaneously, fill the pool in the same time during which the pool is filled by the third pipe alone. The second pipe fills the pool five hours faster than the first pipe and four hours slower than the third pipe. Find the time required by each pipe to fill the pool separately.

Answer 1

Let the time taken by the first pipe be x hours.

Second pipe fills the pool 5 hours faster than the first:

Time of second pipe = x − 5

Second pipe fills the pool 4 hours slower than the third:

Time of third pipe = (x − 5) − 4 = x − 9

`1/x + 1/(x-5) = 1/(x-9)`

Take LCM x(x − 5) (x − 9):

(x − 5) (x − 9) + x(x − 9) = x(x − 5)

(x² − 14x + 45) + (x² − 9x) = x² − 5x

2x² − 23x + 45 = x² − 5x

x² − 18x + 45 = 0

(x − 15) (x − 3) = 0

x = 15 or x = 3

Reject x = 3

First pipe: x = 15 hours

Second pipe: 15 − 5 = 10 hours

Third pipe: 15 − 9 = 6 hours

First pipe fills the pool in 15 hours

Second pipe fills the pool in 10 hours

Third pipe fills the pool in 6 hours