You have 40 minutes to exercise at the gym, and you want to burn 300 calories total using both machines. How much time should you spend on each machine?

Answer 1

You definitely need to know more about how the rate of calorie burn for your two machines!

To start off, though, you can find a few things about your exercise goals in this word problem. 300 calories in 40 minutes can be set up as a ratio to find out how many calories per hour or calories per minute you are trying for:

300 calories /40 minutes = x calories/60 minutes for calories per hour (you are aiming for 450 calories burned per hour)

300 calories / 40 minutes = 7.5 calories per minute if you want to look at it that way instead.

One version of this problem that I found online completes the setup this way [CAUTION: your problem from school might not be the same. In that case please just use this an example]:

1. First machine is 8 calories per minute
2. Second machine is 6 calories per minute

This allows us to set up a system of equations. The first equation will be for calories burned:

8x + 6y = 300

x is minutes on the 8 calorie per minute machine; y is minutes on the 6 calories per minute machine.

A second equation simply shows that the total minutes add up to 40:

x + y = 40

Now you can use substitution, elimination, or linear combinations to solve the system. I'll use substitution to rewrite the second equation:

x = 40 - y

Now substituting into the first equation:

8(40 - y) + 6y = 300

320 - 8y + 6y = 300

2y = 20

y = 10

From there, you can figure out what x is, and then be able to understand how many minutes would be spent on each machine!

Best of luck!

Nate

Answer 2

In order to solve this problem, you would need some estimate for the amount of calories burned per minute on each machine. Would you mind editing your question or posting a new one with this updated info?

If I did my research correctly, the info for this problem is:

8 cal. per minute on the first machine

6 cal. per minute on the second machine.

Let's name two variables: x being the amount of time you spend on the first machine, and y being the amount of time you spend on the second one. We know that you only have 40 minutes, so x + y = 40.

We also know that you want to burn 300 calories, which means we can use the calorie per minute estimates times x and y and set it equal to 300. So the second equation would look something like:

8x + 6y = 300.

Now that we have two equations, we can solve using substitution.

x+y=40

x=40-y

8(40-y) + 6y =300

320 - 8y + 6y =300

-2y=-20

y=10

This leaves x to be 30.

You should spend 30 minutes on machine 1 and 10 minutes on machine 2.