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 = (y3 - 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) = (y3 - 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) = (y3 - y) we'll divide both sides by (y - 1), so
l • w • [(y - 1)] ÷ [(y - 1)] = [(y3 - y)] ÷ [(y - 1)] now we have...
l • w = [(y3 - 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: (y3 - 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