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