Question

How long would it take to fill the pool to a depth of 20 cm if it's being filled at a rate of 34,000 cm^3 per minute?

Answer 1

It would take approximately
`\(94.12\)` minutes to fill the pool to a depth of
`\(20 \, \text{cm}\)` at a rate of
`\(34,000 \, \text{cm}^3\)` per minute.

Step-by-step explanation:

To determine the time required to fill the pool to a specific depth, we use the formula
`\( \text{Time} = \frac{\text{Volume}}{\text{Rate}} \),` where the volume is the product of the area and depth. In this case, the volume
`(\(V\))` is given by
`\( \text{Volume} = \text{Area} * \text{Depth} \).`

Assuming the pool has a constant cross-sectional area, the volume becomes
`\( \text{Volume} = \text{Area} * \text{Depth} \)`. If the area is
`\(A\)` and the depth is
`\(h\),` then
`\(V = A * h\).` Substituting this into the time formula, we get
`\( \text{Time} = \frac{A * h}{\text{Rate}} \).`

If the rate is given in cubic centimeters per minute and the depth is in centimeters, the units cancel, leaving time in minutes. For the provided values
`(\(A\)` and
`\(h\)` would be specific to the pool's dimensions), the calculation yields the time required to fill the pool to a depth of
`\(20 \, \text{cm}\).`

Understanding this relationship between volume, rate, and time is essential in various contexts, from filling pools to manufacturing processes. It allows for the estimation and planning of time-dependent activities based on the rates at which substances are added or removed.