Exercise 11 Page 39

We are given that a truck driver averages $60\text{mph}$ while delivering freight, and $45\text{mph}$ when going back. The total driving time is $7$ hours. We want to find how long each trip takes.

To calculate the time each trip takes, we will need to use the Distance Formula. If we let $t$ be the time the shorter trip takes, then the longer trip will take $7-t$ hours, since both trips took $7$ hours in total. By substituting the respective times and rates we can write equations describing the completed distance for both legs of the journey. We know that the completed distances will be the same since the driver takes the same route, only changing the direction. Since $t$ represented the time needed for the driver to reach the delivering site, we know that it took $3$ hours for the truck driver to get there. Let's now calculate the time needed to go back. It took $4$ hours for the driver to get back.