Question

A cylindrical water tank is being filled with a hose. The depth of the water increases by 1 1/4 feet per hour.

Answer 1

Answer: 2 4/5

Your answer would be 2 4/5. Hope this helps.

Step-by-step explanation:

Answer 2

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.