Use the table to answer the question
Time (hours) 0 4 7 9 12
Distance Miles 0 248 449 565 757
The Diaz family went on a road trip for vacation. The table includes a cumulative chart of the time they traveled compared to the distance they drove.
Over which interval was their average speed the fastest [0,4], [4,7], [7,9] or [9,12]? Explain your reasoning by showing steps for finding the average rate of change for each interval.
(6 points)
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Over the first interval [0,4] the average rate of change
is (248-0)/(4-0) = 248/4 = 62 miles per hour.
Over the second interval [4,7] the average rate of change is (449-248)/(7-4) = 201/3 ≈ 67 miles per hour.
Over the third interval [7,9] the average rate of change is (565-449)/(9-7) = 116/2 = 58 miles per hour.
Over the fourth interval [9,12] the average rate of change is (757-565)/(12-9) = 192/3 ≈ 64 miles per hour.
Therefore, the fastest average speed was during the [4,7] interval, with an average rate of 67 miles per hour.