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)

Answer 1

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.