To determine how quickly the water level increases in the pool, we need to find the rate of the increase in feet per hour. We will break down the mixed numbers into improper fractions to make our calculation clearer.
1. Convert the mixed numbers to improper fractions:
- The time taken to fill the pool is given as [tex]\(1\frac{1}{3}\)[/tex] hours.
[tex]\[
1\frac{1}{3} = 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \text{ hours}
\][/tex]
- The depth of the pool is given as [tex]\(2\frac{2}{4}\)[/tex] feet.
[tex]\[
2\frac{2}{4} = 2 + \frac{2}{4} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \text{ feet}
\][/tex]
2. Calculate the rate of water level increase:
To find the rate, we divide the depth of the pool by the time taken to fill it.
[tex]\[
\text{Rate of increase} = \frac{\text{Pool depth}}{\text{Hours to fill}} = \frac{\frac{5}{2}}{\frac{4}{3}}
\][/tex]
Dividing one fraction by another involves multiplying by the reciprocal:
[tex]\[
\frac{\frac{5}{2}}{\frac{4}{3}} = \frac{5}{2} \times \frac{3}{4} = \frac{5 \times 3}{2 \times 4} = \frac{15}{8}
\][/tex]
3. Simplify the result:
[tex]\[
\frac{15}{8} = 1.875 \text{ feet per hour}
\][/tex]
Therefore, the water level in the pool increases at a rate of [tex]\(1.875\)[/tex] feet per hour.
