Burning 300 Calories

Date: 10/15/97 at 17:29:34
From: John
Subject: Systems of equations

In my math class I have a page of homework that was pretty easy until 
I came across the folowing question: 

Liam burns 8.3 Cal/min when using a rowing machine, and 5.9 CAl/min 
when using an exercise bike. He plans to exercise for 45 minutes and 
wants to burn 300 Calories.  How many minutes should he spend on each 
machine?

I understand the different types of systems of equations and how 
to use them; however, I have no clue where to start. Can you help?

Thanks,
John

Date: 10/25/97 at 16:15:13
From: Doctor Melissa
Subject: Re: Systems of equations

I would start at the end of the word problem. 

What information are you looking for? The minutes he should spend on 
each machine. You know the total number of minutes is 45, but you're 
looking for two numbers that make 45 when you add them together. So 
you could assign x to the number of minutes he spends rowing, and that 
makes the number of minutes he spends biking 45-x. Then you need to 
set up an equation to work in the desired number of calories burned. 

In order to get to 300 calories, you'd add the number of calories 
burned in rowing to the number of calories burned in biking. In terms 
of x, 8.3x is the calories burned rowing, while 5.9(45-x) is the 
calories burned biking. So your equation would read:

   8.3x + 5.9(45-x) = 300

Can you take it from there? (Just don't forget that you're looking for 
_two_ numbers. That was my most frequent oversight with this type of 
problem...)

-Doctor Melissa,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/