Final answer:
The town swimming pool filled at a rate of 750 gallons per hour. To fill a private pool of 80,000 L with a hose delivering 60 L/min, it would take approximately 22.22 hours. Using a river flowing at 5000 m³/s, the pool would fill almost instantly.
Step-by-step explanation:
To calculate the rate at which the town swimming pool fills, we divide the total amount of water by the total time it took to fill that volume. The pool contains 18,000 gallons of water and took 24 hours to fill. Therefore, the rate of filling is 18,000 gallons / 24 hours which equals 750 gallons per hour. So, the pool was filled at a rate of 750 gallons per hour.
Calculating Time to Fill Different Sized Pools
(a) To estimate the time to fill a private swimming pool with a capacity of 80,000 L using a garden hose that delivers 60 L/min, we first convert the rate of the hose to L/hour:
60 L/min × 60 min/hour = 3,600 L/hour. Next, we divide the capacity of the pool by the rate of the hose:
80,000 L / 3,600 L/hour ≈ 22.22 hours.
(b) To estimate the time it would take if you diverted a moderate size river flowing at 5000 m³/s into the pool, we first need to convert cubic meters per second to liters:
5000 m³/s × 1,000,000 L/m³/s = 5,000,000,000 L/s. With this rate, filling an 80,000 L pool would take a negligibly small fraction of a second, so it's not a practical scenario.