Use the table to answer the question.

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 determine which interval had the fastest average speed, we need to analyze the distance traveled over the time intervals provided. The average speed can be calculated using the formula:

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

Now, let's evaluate each interval:

  1. Interval [0, 4]:

    • Calculate the distance traveled from time 0 to 4.
    • Let’s say the distance at time 0 is \(d_0\) and at time 4 is \(d_4\).
    • Distance = \(d_4 - d_0\)
    • Time = 4 - 0 = 4
    • Average Speed = \(\frac{d_4 - d_0}{4}\)
  2. Interval [4, 7]:

    • Distance from time 4 to 7: \(d_7 - d_4\)
    • Time = 7 - 4 = 3
    • Average Speed = \(\frac{d_7 - d_4}{3}\)
  3. Interval [7, 9]:

    • Distance from time 7 to 9: \(d_9 - d_7\)
    • Time = 9 - 7 = 2
    • Average Speed = \(\frac{d_9 - d_7}{2}\)
  4. Interval [9, 12]:

    • Distance from time 9 to 12: \(d_{12} - d_9\)
    • Time = 12 - 9 = 3
    • Average Speed = \(\frac{d_{12} - d_9}{3}\)

To determine which interval had the highest average speed, you need the specific distances traveled from the data in your table.

  • Compare the average speeds calculated for the above intervals.
  • The interval with the highest average speed corresponds to the fastest speed.

If you provide the actual distance values from the cumulative distance chart in your table, I can assist you in making these calculations.