Question

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)

Answer 1

To determine the fastest average speed, we need to calculate the average speed for each interval.

1. Interval [0, 4]:
   Distance = 248 - 0 = 248 miles,
   Time = 4 - 0 = 4 hours,
   Average Speed = 248/4 = 62 miles per hour.

2. Interval [4, 7]:
   Distance = 449 - 248 = 201 miles,
   Time = 7 - 4 = 3 hours,
   Average Speed = 201/3 = 67 miles per hour.

3. Interval [7, 9]:
   Distance = 565 - 449 = 116 miles,
   Time = 9 - 7 = 2 hours,
   Average Speed = 116/2 = 58 miles per hour.

4. Interval [9, 12]:
   Distance = 757 - 565 = 192 miles,
   Time = 12 - 9 = 3 hours,
   Average Speed = 192/3 = 64 miles per hour.

The fastest average speed occurred during the interval [4, 7] at 67 miles per hour.