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### 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/
```
Associated Topics:
Middle School Word Problems

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