Section: Math Section 2

22) Stephanie drove at an average rate of 50 miles per hour for two hours and then increased her average rate by 50% for the next 3 hours. Her average rate of speed for the 5 hours was t miles per hour. What is the value of t?

1. 55 mph
2. 60 mph
3. 65 mph
4. 70 mph
5. 75 mph

The average rate of speed is the total distance traveled divided by the total hours traveled. Melanie drove at 50 miles per hour for 2 hours, for a total of 50 x 2 or 100 miles. If she increased her speed by 50%, then she increased her speed by 50% of 50, or 25, so her new speed was 50 + 25 = 75. So, she drove at 75 miles per hour for the next 3 hours, for a total of 75 x 3 = 225 miles. She went 100 miles and then 225 miles, for a total of 325 miles, and she drove for 2 hours and then for 3 hours, for a total of 5 hours. Her average rate for the trip was 325 miles divided by 5 hours, or 65 miles per hour.