To determine how long it will take for the bathtub to fill with 11,000 ounces of water, we need to follow these steps:
1. **Calculate the fill rate in ounces per second.**
Given the fill rate is 72 cubic inches per second (inch³/second) and the density of water is 0.58 ounces per cubic inch (ounce/inch³), we multiply these two quantities to get the fill rate in ounces per second:
Fill rate (ounces/second) = Fill rate (inch³/second) * Water density (ounces/inch³)
Fill rate (ounces/second) = 72 * 0.58
2. **Calculate how long it will take until the tub is filled with 11,000 ounces of water.**
The time it takes (in seconds) will be the total amount of water the tub can hold divided by the fill rate (in ounces per second).
Fill time (seconds) = Water volume (ounces) / Fill rate (ounces/second)
Fill time (seconds) = 11,000 / (Fill rate in ounces/second from step 1)
Now, we'll perform the calculations:
1. **Calculate the fill rate in ounces per second.**
Fill rate (ounces/second) = 72 inch³/second * 0.58 ounces/inch³
Fill rate (ounces/second) = 41.76 ounces/second
2. **Calculate how long it will take to fill the tub with 11,000 ounces of water.**
Fill time (seconds) = 11,000 ounces / 41.76 ounces/second
Fill time (seconds) = 263.26 seconds
To express the answer to the correct number of significant figures, we need to round it to the nearest whole number since our initial data (fill rate, density, and water volume) are given with no more than two or three significant figures. Given that fill times are generally not precise to fractions of a second in practical situations, rounding to a whole number is appropriate.
Fill time (seconds) rounded to the nearest whole number = 263 seconds
Therefore, it will take 263 seconds to fill the bathtub with 11,000 ounces of water when rounding to the appropriate number of significant figures.
