The rate of change in this scenario can be found by calculating the average speed over the time period. To do this, we look at the total miles run and the total hours taken.
You ran 3 miles in the first hour and then you ran 6 miles in the total of two hours. This means that from hour one to hour two, you covered an additional 3 miles (6 miles total – 3 miles already completed). Therefore, the distance traveled in that hour was.
Total Distance = 6 miles
Total Time = 2 hours
Rate of Change (Average Speed) = Total Distance / Total Time = 6 miles / 2 hours = 3 miles per hour.
So, the rate of change of your running speed over the two hours is 3 miles per hour.