# Related Rates again ?

1. May 22, 2006

### Rizzice

Related Rates.. again......?

A swimming pool is 50 feet long and 20 feet wide. Its depth varies uniformly from 2 feet at the shallow end to 12 feet at the deep end. (The figure shows a cross-section of the pool.) Suppose that the pool is being filled at the rate of 1000 gal/min. At what rate is the depth of water at the deep end increasing when the depth there is 6 feet? (One gallon of water occupies a volume of approximately 0.1337 cubic feet.)

So first of all, I can't even picture what this is supposed to look like when I draw it. Supposedly this is a related rates problem, but this doesn't go with any of the equations I've used so far (pretty much just volume equation and pythagorean theorem equation).. I don't know what I'm supposed to do, could anyone at least help me get started or walk me through? I'd appreciate it..

2. May 22, 2006

### arunbg

Just to get you started, the shape of the swimming pool is similar to a wedge or a triangular block with a cuboidal top . How can you find the volume of this block given the dimensions ?
Hint:Find the area of the triangular and rectangular cross sections of the pool.

Arun