Hello, Ron!

A swimming pool is 25 ft wide, 60 ft long, 3 ft deep at the shallow end, and 15 ft at its deepest point.

If the pool is being filled at a rate of 800 ft³/min, at what rate is the water level rising

when the depth at the deepest point is 5ft?

Side view of the pool . . . Ignore the top 3 feet. Code:

: - - - - 60 - - - - - :
- *-----------------------*
: | x *
: - +---------------*
12 : |:::::::::::*
: y |:::::::*
: : |:::*
- - *

The area of the water is: .

From similar right triangles, we have: .

The area of the water is: .

The volume of the water is: .

Differentiate with respect to time: .

We are given: ft³/min and

So we have: .

Therefore: . ft/min.