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 the interval with the fastest average speed, we calculate the average speed for each interval by dividing the change in distance by the change in time.

  1. Interval [0,4]: \[ \text{Average speed} = \frac{248 - 0}{4 - 0} = \frac{248}{4} = 62 \text{ mph} \]

  2. Interval [4,7]: \[ \text{Average speed} = \frac{449 - 248}{7 - 4} = \frac{201}{3} \approx 67 \text{ mph} \]

  3. Interval [7,9]: \[ \text{Average speed} = \frac{565 - 449}{9 - 7} = \frac{116}{2} = 58 \text{ mph} \]

  4. Interval [9,12]: \[ \text{Average speed} = \frac{757 - 565}{12 - 9} = \frac{192}{3} = 64 \text{ mph} \]

The fastest average speed was during the interval [4,7], where the average speed was approximately 67 mph.