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.
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Interval [0,4]: \[ \text{Average speed} = \frac{248 - 0}{4 - 0} = \frac{248}{4} = 62 \text{ mph} \]
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Interval [4,7]: \[ \text{Average speed} = \frac{449 - 248}{7 - 4} = \frac{201}{3} \approx 67 \text{ mph} \]
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Interval [7,9]: \[ \text{Average speed} = \frac{565 - 449}{9 - 7} = \frac{116}{2} = 58 \text{ mph} \]
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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.