Question

You have 48 minutes to exercise at the gym. The elliptical trainer burns 9 calories per minute, while the treadmill burns 8 calories per minute. You want to burn 400 calories total using both machines. How much time should you spend on each machine

Answer 1

16 minutes on the elliptical trainer and 32 minutes on the treadmill.

Explanation:

We have the following relation for the training in both machines:

`400 cal = 9 cal/min*t_(1) + 8 cal/min*t_(2)` (1)

Where:

t₁: is the time spent on the elliptical trainer

t₂: is the time spent on the treadmill

With:

`t_(1) + t_(2) = 48 min` (2)

From equation (2) we have:

`t_(1) = 48 min - t_(2)` (3)

By entering equation (3) into (1):

`400 cal = 9 cal/min*(48 min - t_(2)) + 8 cal/min*t_(2)`

`400 cal = 432 cal - 9 cal/min*t_(2) + 8 cal/min*t_(2)`

`t_(2) = (32 cal)/(1 cal/min) = 32 min`

Now, we can find t₁:

`t_(1) = 48 min - t_(2) = 48 min - 32 min = 16 min`

Therefore, you should spend 16 minutes on the elliptical trainer and 32 minutes on the treadmill.

I hope it helps you!