To determine how long it will take for the bathtub to fill with 58 ounces of water given the data provided, follow these steps:
1. Identify the given rates and target:
- The filling rate of the water is 72 cubic inches per second.
- The density of water is 0.58 ounces per cubic inch.
- The target amount of water to be filled is 58 ounces.
2. Calculate the necessary volume of water to achieve the target weight in ounces:
- Since the density is 0.58 ounces per cubic inch, we use the formula:
[tex]\[
\text{Volume} = \frac{\text{Target weight}}{\text{Density}}
\][/tex]
[tex]\[
\text{Volume} = \frac{58 \text{ ounces}}{0.58 \text{ ounces/inch}^3}
\][/tex]
- This yields a volume of 100.0 cubic inches.
3. Calculate the time needed to fill this volume of water:
- Given the filling rate, we use the formula:
[tex]\[
\text{Time} = \frac{\text{Volume}}{\text{Filling rate}}
\][/tex]
[tex]\[
\text{Time} = \frac{100.0 \text{ inch}^3}{72 \text{ inch}^3/\text{second}}
\][/tex]
- This results in approximately 1.39 seconds.
Therefore, it will take approximately 1.39 seconds to fill the bathtub with 58 ounces of water.
