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?'

If all the pumps are operating simultaneously, they will fill the pool in 25 hours.

Step-by-step explanation:

Step 1; The first pump fills a third of the pool in 2.5 hours. We need to find the rate at which pump 1 fills water in the tank. The capacity of the tank is 2,550 gallons. So

Pump 1 fills 1/3 × 2550 = 850 gallons in 2.5 hours. We need to determine how much water pump 1 pumps into the tank in 1 hour.

If it fills 850 gallons in 2.5 hours, in 1 hour it fills 850/3 = 340 gallons per hour.

Step 2; The second pump fills a fifth of the pool in 5 hours 6 minutes. 5 hours 6 minutes is 5 1/10 hours = 5.1 hours. We need to find the rate at which pump 2 fills water in the tank. The capacity of the tank is 2,550 gallons. So

Pump 2 fills 1/5 × 2550 = 510 gallons in 5.1 hours. We need to determine how much water pump 2 pumps into the tank in 1 hour.

If it fills 510 gallons in 5.1 hours, in 1 hour it fills 510/5.1 = 100 gallons per hour.

Step 3; The third pump drains 338 gallons in 1 hour. So the third pump drains water at a rate of 338 gallons an hour.

Step 4; So the first and second pump fill the water, so

The water filled in an hour = 340 + 100 = 440 gallons an hour.

The third pump drains water, so

The water drained in an hour = 338 gallons.

So the difference in water in the tank in 1 hour = 440 - 338 = 102 gallons are filled in 1 hour.

Since the capacity is 2,550 gallons,

The time taken to fill the tank = 2,550/ 102 = 25 hours. So with all three pumps working together, the pumps will fill the tank in 25 hours.

step-by-step explanation: