You are trying to maintain a healthy lifestyle. You eat a well-balanced diet and follow a regular schedule of exercise. One of your favorite exercise activities is a combination of walking and jogging in your nearby park.

On one particular day, it takes you 1.3 hours to walk and jog a total of 5.5 miles in the park. You are curious about the amount of time you spent walking and the amount of time you spent jogging during the workout.

Let x represent the time you walked and y represent the time you jogged.

1. What is the equation, using x and y, for the total time of your walk/jog workout in the park.

2. a. If you walk at 3 miles per hour, what is the expression that represents the distance you walked.

b. If you jog at 5 miles per hour, what is the expression that represents the distance you jogged.

c. What is the equation for the total distance you walked/jogged in the park.

The situation just described can be represented by the following system.

Note that each equation in this system is in standard form. One approach to solving this system is to solve each equation for one variable in terms of the other and then use the substitution method.

3. a. Solve each of the equations in the system above for y.

b. Solve the system in part a using the substitution method.