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### Speed, Distance, and Time

```
Date: 19 Jun 1995 12:43:23 -0400
From: carla howard
Subject: Speed

If your speedometer is incorrect, and you travel one mile in 45 seconds,
how fast are you driving?

Carla
```

```
Date: 19 Jun 1995 14:23:29 -0400
From: Dr. Ethan
Subject: Speed

Hey Carla,

If your speedometer is incorrect, and you travel one mile in
45 seconds, how fast are you driving?

TOO FAST!

No, just teasing.  Let's figure it out.

When we are done we want miles per hour.  Right now we have miles per
second.  So if we go one mile in 45 seconds, as a fraction that looks like

1 mile
-------
45 seconds

Let's change the time (denominator) to hours.  First we need to get it
into minutes.

Well, since there are 60 seconds in a minute, we can just multiply the
fraction by 60 seconds per minute.  (We haven't changed the value of
the fraction because 60 seconds is the same amount of time as one minute.)

So now it looks like this...

1 mile         60 seconds
---------   *  ----------
45 seconds      1 minute

One more step.

To go from minutes to hours we do almost the same thing. We multiply
by 60 minutes per hour and then the whole thing looks like this.

1 mile           60 seconds      60 minutes
----------   *   -----------  *   ----------
45 seconds       1 minute           1 hour

Now you multiply all the numbers together and cancel whatever units
you can, and whatever doesn't cancel are the units that you keep.
In our example the units that do not cancel are mile and hour, so those
are the units that we want to keep.

So the answer I get when I plug the numbers into a calculator is
80 miles per hour.

As I said before, way too fast.

Hope this helps.  If you do not understand what I did then please write back
and I will explain again.

Ethan  - Doctor On Call
```
Associated Topics:
Middle School Word Problems

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