Question

You have 40 minutes to exercise at the gym, and you want to burn 300 calories total using both machines. How much time should you spend on each machine?Elliptical Trainer: 8 calories per minuteStationary Bike: 6 calories per minuteYou should spend ____ minutes on the elliptical trainer and ____ minutes on the stationary bike.

Answer 1

We have 40 minutes to exercise, and we want to burn 300 calories.

The elliptical trainer burns 8 cal/min and the stationary bike burns 6 cal/min.

We can write the total amount of calories burned as:

$8x+6y=300$

x: minutes in the elliptical trainer.

y: minutes in the stationery bike.

We also know that the total amount of minutes is 40, so we can write:

$x+y=40$

We can write y in function of x, and then solve the first equation:

$x+y=40\longrightarrow y=40-x$$\begin{gathered} 8x+6(40-x)=300 \\ 8x+240-6x=300 \\ 2x=300-240 \\ 2x=60 \\ x=\frac{60}{2} \\ x=30 \end{gathered}$

Then, for x=30, the value of y is:

$y=40-x=40-30=10$

You should spend

30 minutes on the elliptical trainer and

10 minutes on the stationary bike.