Question

Your classmate is starting a new fitness program. He is planning to ride his bicycle 50 minutes every day. He burns 5 calories per

minute bicycling at 11 mph and 8.75 calories per minute bicycling at 15 mph. How long should he bicycle at each speed to burn 400
calories?
He should bicycle for _
minutes at 11 mph and _
minutes at 15 mph.

Answer 1

Your classmate should bicycle for 10 minutes at 11 mph and 40 minutes at 15 mph to burn a total of 400 calories.

Step-by-step explanation:

To solve how long your classmate should bicycle at each speed to burn 400 calories, we set up a system of equations using the given calorie-burning rates. Let x be the time in minutes bicycling at 11 mph and y be the time in minutes bicycling at 15 mph.

The total calories burned from both speeds should be equal to 400 calories, which gives us two equations:

1. 5x + 8.75y = 400
2. x + y = 50

Multiplying the second equation by 5 and subtracting it from the first equation:

5x + 8.75y = 400

- (5x + 5y = 250)

We get:

3.75y = 15

Dividing by 3.75:

y = 40 minutes at 15 mph

Using the second equation, we substitute the value of y to find x:

x + 40 = 50

x = 10 minutes at 11 mph

Your classmate should bicycle for 10 minutes at 11 mph and 40 minutes at 15 mph to burn 400 calories.