Algebra Name:______________________________
2.5 Distance, Rate, Time Problems

1. Leaving from her house, Mary leaves Pittsburgh in her car traveling towards Cleveland at 3 PM. She travels at an average rate of 30 mi/h. Mary’s brother Jack leaves the house an hour later and follows the same route as Mary. He travels at an average rate of 60 mi/h. How long will it take Jack to catch up to Mary?

Draw a diagram and complete a table (rate ⋅ time = distance) to help you visualize the information.

Define your variables.

Write an equation and solve (use your diagram and table to set up equation).

2. A train leaves the train station at 1 PM traveling at an average rate of 60 mi/h. A second train leaves the same station an hour later. It travels at a rate of 96 mi/h. How long will it take the second train to catch up to the first?

3. On Jerry’s way to work in the morning, he was only able to travel at a rate of 20 mi/h because of traffic. On his drive home, he averaged 40 mi/h. If his total travel time was 1 hours, how long did it take him to drive to work?

4. Suppose you hike up a hill at a rate of 4 mi/h. You hike back down the hill at 6 mi/h. The total time you spent on the hiking trip was 3 hours. How much time did it take you to hike up the hill?

6. Sarah and John leave Butler traveling in opposite directions on a straight road. Sarah drives 12 mi/h faster than John. After two hours, they are 176 miles apart. Find Sarah’s rate and John’s rate.