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

Answer:

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

Step-by-step 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):

$400 cal = 9 cal/min*(48 min - t_{2}) + 8 cal/min*t_{2}$  

$400 cal = 432 cal - 9 cal/min*t_{2} + 8 cal/min*t_{2}$

$t_{2} = \frac{32 cal}{1 cal/min} = 32 min$

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!