Thread: Related Rates

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 ft^3/min,
at what rate is the water level rising when the depth at the deepest point is
5ft.

I'm stuck in this exercise. I just need a tip for the exercise. Thanks for you
help.

I did this:
Let x feet be the wide, and y the long, t for time measured in minutes.

dx/dt= 25 ft and I need to find dy/dt when y = 60ft.

I know that I have to write an equation that relates the various quantities of
the problem. But I don't know what equation I should put.

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.

I have that idea but I was confussed. But THANKS A LOT!!!