Question

You have 48 minutes to exercise at the gym. The elliptical trainer bums 9 calories per minute,while the treadmill bums 8 calories per mirnute. You want to bum 400 calories total using bothmachines. How much time should you spend on each machine?

Answer 1

Let:

x = Time spent in the elliptical

y = Time spent in the treadmill

You have 48 minutes, so:

x + y = 48

And you want to burn 400 calories total using both, the elliptical burns 9 per minute and the treadmill burns 8 per minute, so:

9x + 8y = 400

We have a 2x2 system of equations:

x + y = 48

9x + 8y = 400

Let:

x + y = 48 (1)

9x + 8y = 400 (2)

From (1) let's solve for x:

x = 48 - y (3)

Replace (3) into (2)

9(48 - y) + 8y = 400

432 - 9y + 8y = 400

432 - y = 400

Solving for y:

-y = 400 - 432

-y = -32

y = 32

Replace the value of y into (3)

x = 48 - 32 = 16

therefore you should spend 16 min in the elliptical and 32 min in the treadmill