Three Freighters

Date: 10/11/97 at 14:15:59
From: alan smith
Subject: Math word problem

I have been trying to solve the following math question for several 
days. I believe an algebraic equation is necessary to solve it and I 
am unable to find the appropriate equation. Could you please show me 
the solution to this question using all the steps?                 

Three freighters leave St. John's, Newfoundland, for Montreal, Quebec 
at the same time. One ship takes 20 days to make the round trip, 
another ship takes 16 days, and the final ship takes 12 days. If
these ships continously make this round trip between St. John's and 
Montreal, how many trips would each freighter have to make so that all 
three ships are again in port at the same time?

Melissa-Ann W.

Date: 10/11/97 at 21:10:44
From: Doctor Scott
Subject: Re: Math word problem

Hi Melissa-Ann

Great question! You have probably learned that there are a number of 
ways to approach a problem when you're not sure of the answer. One of 
my favorites is to build a table. Sometimes when you build a table you 
can see some patterns and relationships that will help you to create 
an algebraic equation, if that's what really is necessary.  

Consider a table that shows the day on which each ship LEAVES on its 
round trip:


Ship         Trip 1    Trip 2    Trip 3
 1             0         20        40         etc.
 2             0         16        32         etc.
 3             0         12        24         etc.

Then, continue the chart until you find that all three ships are 
leaving at the same time.

This problem is a great example of the need to use the Least Common 
Multiple of the numbers. Remember that the LCM of three numbers (which 
you probably learned about when you were studying fractions) is the 
smallest number that all three numbers go into with no remainder.  
This is exactly what you are looking for in this problem!

-Doctor Scott,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/