Final answer:
To fill a pool of 80,000 liters using a 60 L/min garden hose would take about 1333.33 minutes or 22.22 hours. Diverting a river at 5000 m³/s would fill the same pool in about 0.016 seconds, highlighting the difference between natural and human-controlled water flow rates. None of the options are correct.
Step-by-step explanation:
Estimation of Filling Time for a Swimming Pool
To estimate the time it would take to fill a private swimming pool with a capacity of 80,000 liters using a garden hose that delivers 60 liters per minute, one can use the formula: time (minutes) = volume (liters) ÷ rate (liters/minute).
(a) The calculation would be 80,000 L ÷ 60 L/min = 1333.33 minutes, or approximately 22.22 hours.
(b) If one could divert a moderate-sized river, flowing at 5000 cubic meters per second, into the pool, the calculation changes drastically. With 1 cubic meter equaling 1,000 liters, the rate in liters per second is 5000 m³/s × 1000 L/m³ = 5,000,000 L/s. Thus, it would take merely 80,000 L ÷ 5,000,000 L/s = 0.016 seconds to fill the swimming pool. This is an impractical and theoretical calculation, given that diverting a river would likely cause significant overflows and damage, not just filling the pool.
When dealing with large volumes and high flow rates, humans typically use pumps, hoses, and tailored infrastructure to manage and utilize water efficiently for various purposes, including firefighting, agriculture, and domestic water supply. Extreme differences in flow rates demonstrate the vast scale of nature's forces compared to human-made systems. None of the options are correct.