# Video: Using Unit Rate to Compare Elements in a Word Problem

Jennifer wants to burn an extra 2000 calories a week. She can choose between the following exercise classes. Which class burns the most calories per hour? How long would she have to spend in that class to reach her weekly goal?

04:20

### Video Transcript

Jennifer wants to burn an extra 2000 calories a week. She can choose between the following exercise classes. Which class burns the most calories per hour? How long would she have to spend in that class to reach her weekly goal?

Class A lasts one and a quarter hours and burns 600 calories. In class B, 375 calories are burned in 45 minutes. Class C lasts one hour and burns 400 calories. In order to calculate which class burns the most calories per hour, we need to work out the rate of change. As the three durations are different, we can add an extra column to the table to calculate the number of calories burned per hour.

The duration of class C is one hour, and 400 calories are burned. Therefore, she would burn 400 calories per hour. The duration of class B is 45 minutes, which is equal to three-quarters of an hour. As three-quarters is equal to the decimal 0.75, we could say that 45 minutes is equal to 0.75 of an hour. To calculate the rate of change or number of calories burned per hour, we need to divide the total calories burned by the time in hours. For class B, we need to divide 375 by 0.75. This can be done on the calculator, giving us an answer of 500. In class B, Jennifer would burn calories at a rate of 500 per hour.

There is an easier way of working this out if we didn’t have a calculator. We know that in 45 minutes, Jennifer burns 375 calories. We could therefore calculate the number of calories burned in 15 minutes by dividing by three. 300 divided by three is 100, and 75 divided by three is 25. Therefore, Jennifer would burn 125 calories in 15 minutes. Adding 45 minutes and 15 minutes gives us 60 minutes, and adding 375 to 125 calories gives us 500 calories. As 60 minutes is equal to one hour, this proves that our answer for class B was correct. Jennifer would burn 500 calories per hour.

We could use a similar method to this for class A, starting with 600 calories in one and a quarter hours or 75 minutes. However, the quicker way to work out the number of calories burned per hour for class A would be to divide 600 by one and a quarter. This is the same as dividing 600 by 1.25. This is equal to 480. Therefore, Jennifer burns 480 calories per hour in class A. The largest of these three values is 500. We can therefore conclude that class B burns the most calories per hour.

The second part of the question asks us how long Jennifer would have to spend in that class to reach a weekly goal of burning 2000 calories. We can calculate the time she would need to spend by dividing the total calories she wants to burn by the number of calories burned per hour. We need to divide 2000 by 500. Both the numerator and denominator are divisible by 100, leaving us with 20 divided by five. As 20 divided by five is equal to four, Jennifer would need to spend four hours in class B to burn 2000 calories.