Question

In the following exercises, translate to a system of equations and solve.

Shelly spent 10 minutes jogging and 20 minutes cycling and burned 300 calories. The next day, Shelly swapped times, doing 20 minutes of jogging and 10 minutes of cycling and burned the same number of calories. How many calories were burned for each minute of jogging and how many for each minute of cycling?

Short answer

The amount of calories burned by jogging is 10 and amount of calories burned by cycling is 10.

Step-by-step solution

Step 1. Given Information   

The given data is that Shelly spent 10 minutes jogging and 20 minutes cycling and burned 300 calories. The next day, Shelly swapped times, doing 20 minutes of jogging and 10 minutes of cycling and burned the same number of calories.

Step 2. Explanation   

Let the amount of calories burned by jogging be x and amount of calories burned by cycling be y.

Shelly spent 10 minutes jogging and 20 minutes cycling and burned 300 calories that is $10x+20y=300--\left(1\right)$

The next day, Shelly swapped times, doing 20 minutes of jogging and 10 minutes of cycling and burned the same number of calories that is$20x+10y=300--\left(2\right)$

Step 3. Calculation

Rewrite the equation (1) by multiplying it with 2.

$$\begin{gathered} 2(10x+20y)=2\left(300\right) \\ 20x+40y=600--\left(3\right) \end{gathered}$$

Solve the equation (2) and (3) by subtracting equation (2) from equation (3).

$$\begin{gathered} 20x+40y-20x-10y=600-300 \\ 30y=300 \\ y=10 \end{gathered}$$

Substitute the value of y in equation (1) and simplify.

$$\begin{gathered} 10x+20\left(10\right)=300 \\ 10x=100 \\ x=10 \end{gathered}$$