A pool is filled by two pumps and drained by a third pump. The first pump is filling a third of the pool in 2.5 hours. The second pump is filling a fifth of the pool in 5 hours and 6 minutes. The third pump drains 338 gallons hourly. How many hours would it take all the pumps to fill the pool full together, if they operate simultaneously and the pool's capacity is 2550 gallons?

25 h

Step-by-step explanation:

If the pumps work simultaneously you can add the rates, considering the third pump with a negative rate because it is draining the pool.

The rate is calculated as V/t

Where V is the volume filled or drained in a given time

First pump rate = 1/3 * 2550 / 2.5 = 340 gallons / h

5 hours and 6 minutes = 5 + 6/60 = 5.1 h

Second pump rate = 1/5 * 2550 / 5.1 = 100 gallons / h

Third pump rate = - 338 gallons / h

Total rate = 340 + 100 - 338 = 102 gallons / h

Time needed to fill the pump = 2550 / 102 = 25 h