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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 sentences. Like a 9th grader.

1 answer

To find the fastest average speed, we calculate the speed for each interval by using the formula speed = distance/time.

  • For the interval [0, 4], the distance is 248 miles, so the speed is 248 miles / 4 hours = 62 mph.
  • For the interval [4, 7], the distance is 201 miles (449 - 248), so the speed is 201 miles / 3 hours = 67 mph.
  • For the interval [7, 9], the distance is 116 miles (565 - 449), so the speed is 116 miles / 2 hours = 58 mph.
  • For the interval [9, 12], the distance is 192 miles (757 - 565), so the speed is 192 miles / 3 hours = 64 mph.

The fastest average speed was in the interval [4, 7] at 67 mph.