Question 415225: I'm trying to write an algebraic equation to find the volume in gallons for a swimming pool with the following variables:
Deep End = 8ft
Shallow End = 3ft
Length = 20l
Width = 14w
How do I write the equation using the syntax:
Deep end + Shallow end / 2 = Avg. Depth
Avg. Depth * 20l * 14w * 7.48 = Volume in gallons
I know there is a way to write the equation with all of these variables into one equation, but I haven't been able to figure it out so far. I can do it in two equations but I need it in one. I have a hard time writing algebra equations so if someone could help me I would greatly appreciate it.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The pool is 3 feet deep at the shallow end and 8 feet deep at the deep end.
If you assume that the pool is all shallow, then the volume would be 20 * 14 * 3 = 840 cubic feet.
That's just for the shallow part.
Take that shallow part away and you are left with a pool that is 5 feet deep.
This part of the pool gradually increases in depth from 0 feet at the shallow to 5 feet at the deep end.
The gradual increase in depth is the diagonal of a rectangle.
This divides the rectangle into 2 triangles that are equal in area to each other.
The area of the pool that is 5 feet deep is 20 * 14 * 5 = 1400 square feet.
half of that is equal to 700 square feet.
The total volume of the water in the pool is 840 + 700 = 1540 cubic feet.
From google, you get 1 cubic foot = 7.48051948 US gallons
Since you have 1540 cubic feet, that equates to 11520 gallons of water.
The average depth of your pool would be 3 feet for the shallow part of the pool plus half of 5 feet for the deeper end of the pool.
That would be equal to 3 + 5/2 = 3 + 2.5 = 5.5 feet.
5.5 * 20 * 14 * 7.48051948 = 11520 gallons of water.
I believe that's how you would do it.
The first 3 feet have to be added to the average of the depth from 3 feet to 8 feet.
The average of the first 3 feet is equal to 3 feet because it does that all the way across.
The depth from 3 feet to 8 is 5 and half of that is 2.5.
the average depth of the pool is therefore 3 + 2.5 = 5.5 feet.
Tricky little problem but I believe that's how you would do it in this case.
Knowing a little geometry helps.
The average depth being half of the low end and the high end applies to only the bottom 5 feet of the pool.
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