Respuesta :
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.
