Answer:
[tex]2\frac{4}{5}[/tex] hours.
Step-by-step explanation:
We have been given that a cylindrical water tank is being filled with a hose. The depth of the water increases by 1 1/4 ft per hour. We are asked to find the time taken for the water level in the tank to be 3 1/2 ft deep.
[tex]\text{Time}=\frac{\text{Depth}}{\text{Rate}}[/tex]
Let us convert our given mixed fractions into improper fractions as:
[tex]1\frac{1}{4}\Rightarrow\frac{4\times 1+1}{4}=\frac{4+1}{4}=\frac{5}{4}[/tex]
[tex]3\frac{1}{2}\Rightarrow\frac{2\times 3+1}{2}=\frac{6+1}{2}=\frac{7}{2}[/tex]
[tex]\text{Time}=\frac{\frac{7}{2}}{\frac{5}{4}}[/tex]
Using rule [tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}[/tex], we will get:
[tex]\text{Time}=\frac{7\times 4}{2\times 5}[/tex]
[tex]\text{Time}=\frac{7\times2}{1\times 5}[/tex]
[tex]\text{Time}=\frac{14}{5}[/tex]
[tex]\text{Time}=2\frac{4}{5}[/tex]
Therefore, it will take [tex]2\frac{4}{5}[/tex] hours for the water level in the tank to be [tex]3\frac{1}{2}[/tex] feet deep.
