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### Setting Up Equations

```
Date: 11/26/97 at 21:39:22
From: Jessica Shortreed-Hume
Subject: Setting up equations

An airplane travels eight times as fast as a car. The difference in
their speeds is 420 km/h. How fast is each vehicle travelling?

I tried to set up a formula but it won't work no matter what I try.
Help!
```

```
Date: 11/30/97 at 21:57:40
From: Doctor Allan
Subject: Re: Setting up equations

Hello Jessica!

What you need to do is put the information you have into mathematical
equations. Let me help you with the setup - then you can try to do the
math yourself.

Let's call the speed of the car x and the speed of the plane y. We are
told that the speed of the plane is eight times the speed of the car.
This means that

(1) 8x = y

Furthermore we are told that the difference in their speeds is
420 km/h. We get

(2) y-x = 420

Do you understand how I did this part? If you did you are quite close

In equation (1) you are told that every time you see a y, you can
replace it with 8x. So this is what you do in equation (2), enabling
you to get a value for y. This value can be substituted into equation
(1) yielding a value for x.

Since x and y were the speeds of the car and the plane, you can put

I hope this helps. If it doesn't, please write again.

-Doctor Allan,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Equations
Middle School Word Problems

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