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]?

Question

time:0, 4, 7, 9, 12.
hours:0, 248, 449, 565, 757.

Responses

[0, 4]

[4, 7]

[7, 9]

[9, 12]

Answer 1

To find the fastest average speed over the designated intervals, we can calculate the average speed for each interval by using the formula:

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

We will compute this for each interval.

1. Interval [0, 4]:

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

2. Interval [4, 7]:

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

3. Interval [7, 9]:

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

4. Interval [9, 12]:

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

Now, we summarize the average speeds:

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

The fastest average speed is during the interval [4, 7], with an average speed of 67 mph.

Therefore, the answer is: [4, 7].