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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,] [17,91,] or [9,12]? Explain your reasoning in 2 sentences.

Table:
Time (hours): 0, 4, 7, 9, 12
Distance (miles): 0, 248, 449, 565, 757

1 answer

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

For the intervals:

  • [0, 4]: \( \frac{248 - 0}{4 - 0} = 62 \) mph
  • [4, 7]: \( \frac{449 - 248}{7 - 4} = 67 \) mph
  • [7, 9]: \( \frac{565 - 449}{9 - 7} = 58 \) mph
  • [9, 12]: \( \frac{757 - 565}{12 - 9} = 64 \) mph

The fastest average speed was during the interval [4, 7], with an average speed of 67 mph, as it has the highest calculated speed among all intervals.