Final answer:
Calculating the time to fill a swimming pool involves dividing the pool's volume by the flow rate of the water source. For a pool with 80,000 L capacity and a hose with a 60 L/min rate, it would take approximately 22.22 hours. A moderate size river flow would fill the pool almost instantaneously.
Step-by-step explanation:
The question aims to determine the duration required to fill two different capacities of pools with water. Filling a pool or any such container is a practical application of volume and rate calculations within mathematics, particularly when estimating time and capacity. Let's explore this by working through the examples provided.
For a private swimming pool with a capacity of 80,000 liters, using a garden hose that delivers 60 L/min:
- First, determine the total volume that needs to be filled - 80,000 L.
- Next, find the rate at which the water is being delivered - 60 L/min.
- Then, divide the total volume by the rate to find the time in minutes - 80,000 L ÷ 60 L/min = 1333.33 minutes.
- To convert minutes to hours, divide by 60 - 1333.33 min ÷ 60 = 22.22 hours.
In the case of diverting a moderate size river flowing at 5000 m³/s:
- Convert the pool's capacity to cubic meters as 1 m³ = 1000 L, thus 80,000 L = 80 m³.
- With the river's flow rate being 5000 m³/s, it is practically instantaneous for such a vast amount of water to fill the pool.
Through these exercises, we understand the importance of unit conversion and the application of basic arithmetic in real-life scenarios.