Water Main Section LengthsDate: 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/ |
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