8. Use the graph below to answer the following question.
Jane is hiking in a park. The graph represents the distance (miles) she hiked with respect to time (minutes). Over which time interval did she hike the fastest, [0, 6] or [4, 10]. Justify your answer.
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2 points
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The interval [0, 6] was the fastest because the average rate of change was 0.15 mph.
The interval [4, 10] was the fastest because the average rate of change was 0.15 mph.
The interval [0, 6] was the fastest because the average rate of change was 6 mph.
The interval [4, 10] was the fastest because the average rate of change was 6 mph.
To determine which time interval Jane hiked the fastest, we need to compare the average rate of change of distance over time for each interval.
The average rate of change can be calculated by dividing the change in distance by the change in time.
For the interval [0, 6], the change in distance is 1 mile and the change in time is 6 minutes. So, the average rate of change is 1/6 = 0.1667 miles per minute.
For the interval [4, 10], the change in distance is 4 miles and the change in time is 6 minutes. So, the average rate of change is 4/6 = 0.6667 miles per minute.
Comparing the two average rates of change, we can see that the interval [4, 10] had a faster average rate of change.
Therefore, the correct answer is: The interval [4, 10] was the fastest because the average rate of change was 0.6667 miles per minute.