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### Distance/Time

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Date: 12/8/95 at 15:39:32
From: Anonymous
Subject: word problems

Bernice is cycling around a track at 15 mph.  Betty starts at the same
time, but only goes 12 mph.  How many minutes after they start will
Bernice pass Betty if the track is 1/2 mile long?  They are moving in
the same direction.

Please include a variety of other d=rt to help us out on the process of
using formulas to solve for the missing element.  Thank you for your

Mr. Ames
```

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Date: 5/31/96 at 15:49:3
From: Doctor Gary
Subject: Re: word problems

Dear Mr. Ames;

Although distance is in fact the product of rate and time, I much prefer
to be absolutely certain that students understand the DEFINITION of rate
before encouraging (or even permitting) them to use any formulas.  A
rate of speed, as the name implies, is equal to the quotient of distance
divided by time.  Naturally, your equation of:

d  =  rt

follows naturally from the definition of:

r  =  d/t.

Now, on to your story problem, which is an excellent
opportunity to get students talking and thinking about
math, so that they can better understand that formulas
are nothing more than ways of expressing what is

I'd make a game of it, asking the following questions:

If Bernice goes 15 mph, how many miles will she
travel in an hour?

How many times around the 1/2 mile track is that?

If Betty goes 12 mph, how many miles will she travel in an hour?

How many times around the 1/2 mile track is that?

Once students understand that, they should
appreciate that Bernice "laps" (i.e.  catches up to
and passes, or "meets") Betty 6 times every hour, or
once every 10 minutes.

Here are two related questions:  How long does it take
Bruce to circle the same track once at the rate of
3 mph?   How fast would Dave have to walk around a
one-mile track in order to circle it once every twenty
minutes?

-Doctor Gary,  The Math Forum

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Associated Topics:
Middle School Word Problems

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