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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:

(1 point)
Responses

[9, 12]
[9, 12 ]

[4, 7]
[4, 7]

[7, 9]
[7, 9]

[0, 4]

1 answer

To find the interval where the Diaz family had the fastest average speed, we need to calculate the average speed for each time interval given, using the formula:

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

Let's calculate the average speed for each interval:

  1. Interval [0, 4]:

    • Change in distance = 248 miles - 0 miles = 248 miles
    • Change in time = 4 hours - 0 hours = 4 hours
    • Average speed = \( \frac{248}{4} = 62 \) miles per hour

  2. Interval [4, 7]:

    • Change in distance = 449 miles - 248 miles = 201 miles
    • Change in time = 7 hours - 4 hours = 3 hours
    • Average speed = \( \frac{201}{3} = 67 \) miles per hour

  3. Interval [7, 9]:

    • Change in distance = 565 miles - 449 miles = 116 miles
    • Change in time = 9 hours - 7 hours = 2 hours
    • Average speed = \( \frac{116}{2} = 58 \) miles per hour

  4. Interval [9, 12]:

    • Change in distance = 757 miles - 565 miles = 192 miles
    • Change in time = 12 hours - 9 hours = 3 hours
    • Average speed = \( \frac{192}{3} = 64 \) miles per hour

Now, let's summarize the average speeds for each interval:

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

The fastest average speed occurred in the interval [4, 7] where the average speed was 67 miles per hour.

Therefore, the answer is:

[4, 7]