Question

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

How many hours will it take for the water level in the tank to be 3 1/2 feet deep?

Enter your answer as a mixed number in simplest form

Answer 1

Answer: 2 4/5

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

Explanation:

Answer 2

Answer:
`2(4)/(5)` hours

Explanation:

Given: The rate of increase of depth of water =
`1(1)/(4)=(5)/(4)` feet per hour.

Depth =
`3(1)/(2)\ =(7)/(2)\ feet`

Let h be the number of hours the water level in the tank to be
`3(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\ (5)/(4)=((7)/(2))/(h)\\\\\Rightarrow\ (5)/(4)=(7)/(2h)\\\\\Rightarrow5(2h)=4(7)\\\\\Rightarrow h=(28)/(10)=(14)/(5)=2(4)/(5)`

Hence, it will take
`2(4)/(5)` hours for the water level in the tank to be
`3(1)/(2)` feet deep.