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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 1–2 sentences.

(2 points)

1 answer

To determine which interval had the fastest average speed, we calculate the average speed for each interval using the formula: average speed = (change in distance) / (change in time).

  1. For [0,4]: (248 - 0) miles / (4 - 0) hours = 248 / 4 = 62 miles/hour
  2. For [4,7]: (449 - 248) miles / (7 - 4) hours = 201 / 3 = 67 miles/hour
  3. For [7,9]: (565 - 449) miles / (9 - 7) hours = 116 / 2 = 58 miles/hour
  4. For [9,12]: (757 - 565) miles / (12 - 9) hours = 192 / 3 = 64 miles/hour

The fastest average speed was in the interval [4,7], with an average speed of 67 miles/hour.