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 in 1–2 sentences. (2 points)
To determine the interval with the fastest average speed, we need to calculate the average speed for each interval. The average speed is calculated by dividing the distance traveled by the time taken.
For the interval [0,4], the average speed is 248 miles / 4 hours = 62 miles/hour.
For the interval [4,7], the average speed is (449 - 248) miles / (7 - 4) hours = 67 miles/hour.
For the interval [7,9], the average speed is (565 - 449) miles / (9 - 7) hours = 58 miles/hour.
For the interval [9,12], the average speed is (757 - 565) miles / (12 - 9) hours = 64 miles/hour.
Therefore, the fastest average speed was during the interval [4,7] with an average speed of 67 miles/hour.