Adding a 6-Inch Layer of Gravel

Date: 03/13/2003 at 16:25:48
From: Megan
Subject: Can you show me the steps to doing this problem

Your company is constructing a soccer field for a high school. The 
field is 110 yards long and 80 yards wide. You receive the following 
note from your boss:

The Board of Zoning requires that a 6-inch layer of gravel must be 
laid on all athletic fields before topsoil is added, to give adequate 
drainage. Our gravel supplier says that each truck load contains 12 
cubic yards of gravel, at a cost of $9.25/cubic yard delivered.

Calculate how many truckloads of gravel we should order for the soccer 
field and estimate how much it will cost. I need to have your 
background calculations, clearly explained, as well as the total cost 
in order to get budget approval. 

Date: 03/13/2003 at 19:11:05
From: Doctor Ian
Subject: Re: Can you show me the steps to doing this problem

Hi Megan,

Sometimes, it's just the size and the numbers in a problem that make
it seem intimidating.  Let's see if we can reduce your problem to a
smaller one, that will be easier to think about. 

Basically, we're going to cover some surface area to some depth, with 
some stuff. It could be a soccer field, or it could be a Jello mold.  

Suppose we have a Jello mold that is 9 inches by 12 inches, and we
want to put enough Jello in it to cover it to a depth of 2 inches. 
How much Jello _is_ that? 

The shape formed by the Jello will be a rectangular prism, sort of
like a cereal box. The volume of this shape can be computed this way:

  Volume = width * length * depth

Our pan is 9 inches by 12 inches, and we want the Jello to be 2 inches 
deep. So the volume is 

  9 in * 12 in * 2 in = 216 cubic inches

So this is how much Jell-o we need. 

>Calculate how many truckloads of gravel we should order for the 
>soccer field and estimate how much it will cost. I need to have your 
>background calculations, clearly explained, as well as the total cost 
>in order to get budget approval. 

Now, suppose we can buy Jello in packets that make 18 cubic inches. 
How many packets do we need? The answer is however many times we'd
need to add up 18 cubic inches until we end up with 216 cubic inches. 

   (number of packets) * 18 cubic inches = 216 cubic inches

We can get this number by dividing 216 by 18:

  number of packets = 216 / 18

                    = 12

So we need 12 packets.  And if each packet costs, say, 20 cents, then
that will cost 

  12 * 20 cents = 240 cents

                = $2.40

Read this over and let me know if there's any part of it that you
weren't able to follow. If you can follow it all, then you can do the
same thing to solve _your_ problem, because it's basically the same. 
Only the numbers and the units are different. 

There's one tricky part, actually. But it's not _too_ tricky. The 
field is measured in yards, and the trucks are measured in cubic 
yards, but the dept of the gravel is measured in inches. Uh oh! 
There's an easy fix, though: 6 inches is half a foot, so it's 1/6 of
a yard.  

Does this help?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 03/13/2003 at 22:52:05
From: Megan
Subject: Thank you (Can you show me the steps to doing this problem)

Thank you very much for taking the time to break my problem down into 
an easier way of managing it. It helped me out a great deal. I 
understood the problem and was able to figure it out with starting 
with the easier problem first. Thank you for your time. Have a great 
day!