Question

Anna burned 15 calories per minute running for x minutes and 10 calories per minute hiking for y minutes. She spent a total of 60 minutes running and hiking and burning 700 calories. The system of equations shown below can be used to determine how much time Anna spent on each exercie.

Answer 1

Given:

$15x+10y=700$$x+y=60$

where x represents the number of minutes of running and y represents the number of minutes of hiking.

Required:

We need to find the number of minutes for running.

Explanation:

Consider the equation.

$x+y=60$

Subtract x from both sides of the equation.

$x+y-x=60-x$$y=60-x$

Consider the equation.

$15x+10y=700$$Substitute\text{ y=60-x in the equation.}$

$15x+10(60-x)=700$$15x+600-10x=700$$5x+600=700$

Subtract 600 from both sides of the equation.

$5x+600-600=700-600$$5x=100$

Divide both sides of the equation by 5.

$\frac{5x}{5}=\frac{100}{5}$$x=20$

The running time is 20 minutes.

Substitute x =20 in the equation y =60-x.

$60-20=40$

The hiking time is 40 minutes.

Final answer:

The running time is 20 minutes.

The hiking time is 40 minutes.