Use the table to answer the question. Time (hours) 04 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]; [9, 12]; [7, 9]

Answer 1

To find the interval with the fastest average speed, we need to calculate the average speed for each specified time interval using the formula:

\[ \text{Average Speed} = \frac{\text{Change in Distance}}{\text{Change in Time}} \]

Now, we'll break down each interval:

1. Interval [0, 4]

   • Time: 0 to 4 hours
   • Distance: 0 to 248 miles
   • Change in Distance = 248 - 0 = 248 miles
   • Change in Time = 4 - 0 = 4 hours
   • Average Speed = \( \frac{248}{4} = 62 \) miles/hour

2. Interval [4, 7]

   • Time: 4 to 7 hours
   • Distance: 248 to 449 miles
   • Change in Distance = 449 - 248 = 201 miles
   • Change in Time = 7 - 4 = 3 hours
   • Average Speed = \( \frac{201}{3} = 67 \) miles/hour

3. Interval [7, 9]

   • Time: 7 to 9 hours
   • Distance: 449 to 565 miles
   • Change in Distance = 565 - 449 = 116 miles
   • Change in Time = 9 - 7 = 2 hours
   • Average Speed = \( \frac{116}{2} = 58 \) miles/hour

4. Interval [9, 12]

   • Time: 9 to 12 hours
   • Distance: 565 to 757 miles
   • Change in Distance = 757 - 565 = 192 miles
   • Change in Time = 12 - 9 = 3 hours
   • Average Speed = \( \frac{192}{3} = 64 \) miles/hour

Now we compare the average speeds calculated for each interval:

• [0, 4]: 62 mph
• [4, 7]: 67 mph
• [7, 9]: 58 mph
• [9, 12]: 64 mph

The fastest average speed is in the interval [4, 7], with an average speed of 67 miles/hour.