Answer: [tex]2\frac{4}{5}[/tex] hours
Step-by-step explanation:
Given: The rate of increase of depth of water = [tex]1\frac{1}{4}=\frac{5}{4}[/tex] feet per hour.
Depth = [tex]3\frac{1}{2}\ =\frac{7}{2}\ feet[/tex]
Let h be the number of hours the water level in the tank to be [tex]3\frac{1}{2}[/tex] feet deep.
We know that the rate of change of depth of water with respect to time is given by :-
[tex]k=\frac{\text{Depth}}{\text{time}}\\\\\Rightarrow\ \frac{5}{4}=\frac{\frac{7}{2}}{h}\\\\\Rightarrow\ \frac{5}{4}=\frac{7}{2h}\\\\\Rightarrow5(2h)=4(7)\\\\\Rightarrow h=\frac{28}{10}=\frac{14}{5}=2\frac{4}{5}[/tex]
Hence, 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.
