Hi A from Billerica, MA...hope you had a great day at school.

This is a great Algebra/Geometry problem...wish I thought of it myself. This are high school student's favorite kinds of problems...RIGHT?! NOT!!

Alright...I'm going to help you set up the problem however, I won't answer it for you, but give you the hints to solve it. When you do you will have the skill to answer others like it...like a PRO!

Let's begin with the things we know:

Your teacher tells you the height of the swimming pool is: *h* = (y - 1)

Your teacher let's you know the swimming pool volume: *v* = (y^{3} - y)

Now we need to know the formula for calculating to volume, which you should know which is: *l* • *w* • *h* = *v*

What we don't know is the length: *l*

and what we don't know is the length: *w*

Now with what we know, lets substitute the things we know:

*l* • *w* • (y - 1) = (y^{3} - y) Do you see where we are at? Not lost?

So...now were do we go from here? Do you know? What is it your teacher is asking? What is *l * and what is *w*

Let's go back to our rewritten volume equation:

*l* • *w* • (y - 1) = (y^{3} - y) we'll divide both sides by (y - 1), so

**l** • *w* • [(y - 1)] ÷ [(y - 1)] = [(y^{3} - y)] ÷ [(y - 1)] now we have...

*l* • *w* = [(y^{3} - y)] ÷ [(y - 1)]

How would you change this equation to find our what *l* & *w* would be?

Hint: could could see if you can factor the expression: (y^{3} - y)

If you can't fact it...another hint...divide so that *w* = ? and *l* = ?

Try and continue with the problem...if you need any further help contact me on Wyzant