Fencing Two Back Yards

Date: 01/27/2001 at 20:44:46
From: Joanne
Subject: Fencing backyards

The problem my teacher gave me is:

Sarah and JAne want to put a fence around their two rectangular 
back yards, with a single fence separating the yards. The dimensions 
of their back yards are shown in the diagram below.

The price of fencing is $3.00 a foot. The price of the fence includes 
tax.  If Sarah and Jane share the cost of the fence equally, how much 
money will each of them pay?
  
          40'                              40'                   
    '---------------------------------------------------------'
60' '                           '60'                          ' 60'
    '                           '                             '
    '---------------------------------------------------------'
           40'                               40'
                                                                      
              

I don't understand what I'm supposed to do.

Date: 01/29/2001 at 15:00:34
From: Doctor Keith
Subject: Re: Fencing backyards

Hi Joanne,

Let's tackle this problem in three steps. First, we will figure out 
how many feet of fencing we need. Second, we will find out how much 
the fencing costs.  Then we will find Sarah and Jane's cost.

1) How much fencing?
 
We look at the picture and notice that the fencing goes on the 
lines you have drawn. We can thus add the lengths of all the lines. 
There are three sides with length 60 feet, and four sides with length 
40 feet. From this we can set up an addition or a multiplication 
problem to find the total. I will leave this to you. If you have 
questions, write back.

2) Total cost

Every foot costs $3, so if we had 10 feet of fencing it would cost 
3 * 10 = 30 for a total of $30 dollars. We found out how many feet of 
fencing we have in part (1). Now let's calculate how much it will cost 
at $3 per foot. We saw in our little example that you have to multiply 
the feet of fencing times the cost per foot. Set up a multiplication 
problem to find the total cost.  

3) Cost per person

We know that two people (Sarah and Jane) are going to pay equal 
amounts for the fence. We need to divide the cost from part (2) into 
two equal parts. For example, we saw that 10' of fencing costs $30.  
If Sarah and Jane split this evenly, we can use division by 2 to get 
the amount paid by each:

  30 / 2 = 15

so each would pay $15 for 10' of fencing. In your problem, Sarah and 
Jane are buying a lot more fencing.  What would be the division 
problem for your question?

This lets you see how you can solve more complicated problems by 
breaking them into smaller steps you can solve. If you have any more 
questions, or you would like to understand more about this problem, 
write back and I will be glad to help you.

Best wishes,

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