Water Main Section Lengths

Date: 01/09/2003 at 16:12:42
From: Morgan
Subject: Lengths of water main sections

A water main for a street is being laid using a particular kind of 
pipe that comes in either 18-foot sections or 20-foot sections.  The 
designer has determined that the water main will require 14 fewer 
sections of 20-foot pipe than if 18-foot sections are used. Find 
the total length of the water main.

Date: 01/10/2003 at 14:11:33
From: Doctor Ian
Subject: Re: Lengths of water main sections

Hi Morgan,

Assuming that all the pipe gets used in either case, suppose that the
job can be done with some number (call it N) of 20-foot sections of
pipe. Then the total length is

  20*N

We're told that if we use 18-foot sections instead, we'll need 14 more
sections. That is, 

  20*N = 18*(N+14)

Solve this for N, and you'll have the number of 20-foot sections that
will do the job.  

Here's another way to think about it. Suppose we have a bunch of
20-foot sections. Now we cut 2 feet off of each section, so that we
have the same number of 18-foot sections, but less total pipe.  

How much less? To make up the difference, we have to add 14 more
18-foot sections. That works out to 

  14*18 = 252 

extra feet. So now the question is:  If we got rid of 252 feet of
pipe by cutting 2 feet each off of a bunch of sections, how many
sections did we cut? 

And here is another way to ask the same question: How many 2-foot
sections of pipe would we have to put together to get the same length
as 14 18-foot sections?

Does this help? 

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