Hello, ihmth!

1) A swimming pool is 40 ft long, 20 ft wide, 8 ft deep at the deep end

and 3 ft deep at the shallow end. The bottom is rectangular.

If the pool is filled with by pumping water into it at the rate of 100 ft³/min,

how fast is the water level rising when it is 3 ft deep at the deep end? Code:

40
- * - - - - - - - - - - - - - - - - - *
: | |
3 | | 3
: | 40 |
_ * - - - - - - - - - - - - - - - - - *
: | x *
: + - - - - - - - - - - - *
5 |:::::::::::::::::*
: |h::::::::::*
: |:::::*
- *

The pool is filled to a height of feet.

The volume of the water is: .

So we have: . .[1]

From similar right triangles, we have: . .[2]

Substitute [2] into [1]: .

Differentiate with respect to time: . .[3]

We are given: .

Substitute into [3]: .

Therefore, the water is rising at: .