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.

Answer 1

To determine the fastest average speed over the given intervals, we can calculate the average speed for each segment using the formula: speed = (distance at the end of interval - distance at the start of interval) / (time at the end of interval - time at the start of interval).

1. **Interval [0, 4]:**
Speed = (248 - 0) / (4 - 0) = 248 / 4 = 62 mph

2. **Interval [4, 7]:**
Speed = (449 - 248) / (7 - 4) = 201 / 3 = 67 mph

3. **Interval [7, 9]:**
Speed = (565 - 449) / (9 - 7) = 116 / 2 = 58 mph

4. **Interval [9, 12]:**
Speed = (757 - 565) / (12 - 9) = 192 / 3 = 64 mph

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