To find the rate of change for this running situation, we need to calculate the distance covered per unit of time.
Initially, you ran 3 miles in 1 hour. This gives us a rate of:
- Rate for first segment = Distance / Time = 3 miles / 1 hour = 3 miles per hour
Next, we look at the second part of the situation, where you ran 6 miles in 2 hours. The rate for this segment is:
- Rate for second segment = Distance / Time = 6 miles / 2 hours = 3 miles per hour
Now, to get the overall rate of change, we can average these two rates since they are constant. Since both segments yielded the same rate, we conclude that:
- Overall Rate = (3 miles/hour + 3 miles/hour) / 2 = 3 miles per hour
Thus, the rate of change for running 3 miles in one hour and 6 miles in two hours is consistently 3 miles per hour.