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 
to the answer.

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 
your answer back into words once you find x and y.

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/