To solve this problem, we need to calculate Larry's average speed over two different time intervals and then compare those speeds to determine if he sped up or slowed down.
1. Finding the average speed from hour 2 to hour 4:
- First, we calculate the difference in time between hour 2 and hour 4:
[tex]\[
\text{Time difference} = 4 \, \text{hours} - 2 \, \text{hours} = 2 \, \text{hours}
\][/tex]
- Next, we calculate the difference in distance between the distances recorded at hour 2 and hour 4:
[tex]\[
\text{Distance difference} = 27.5 \, \text{miles} - 13.5 \, \text{miles} = 14 \, \text{miles}
\][/tex]
- The average speed is calculated by dividing the distance difference by the time difference:
[tex]\[
\text{Average speed (2 to 4 hours)} = \frac{14 \, \text{miles}}{2 \, \text{hours}} = 7 \, \text{miles per hour}
\][/tex]
2. Finding the average speed from hour 4 to hour 7:
- First, we calculate the difference in time between hour 4 and hour 7:
[tex]\[
\text{Time difference} = 7 \, \text{hours} - 4 \, \text{hours} = 3 \, \text{hours}
\][/tex]
- Next, we calculate the difference in distance between the distances recorded at hour 4 and hour 7:
[tex]\[
\text{Distance difference} = 48.5 \, \text{miles} - 27.5 \, \text{miles} = 21 \, \text{miles}
\][/tex]
- The average speed is calculated by dividing the distance difference by the time difference:
[tex]\[
\text{Average speed (4 to 7 hours)} = \frac{21 \, \text{miles}}{3 \, \text{hours}} = 7 \, \text{miles per hour}
\][/tex]
3. Determining if he sped up or slowed down:
- We compare the average speeds from both intervals:
[tex]\[
\text{Average speed from 2 to 4 hours} = 7 \, \text{miles per hour}
\][/tex]
[tex]\[
\text{Average speed from 4 to 7 hours} = 7 \, \text{miles per hour}
\][/tex]
- Since both average speeds are equal, we determine that Larry maintained the same speed during both intervals.
Therefore, the answers to the questions are:
- Average speed from hour 2 to hour 4: [tex]\(7 \, \text{miles per hour}\)[/tex]
- Average speed from hour 4 to hour 7: [tex]\(7 \, \text{miles per hour}\)[/tex]
- Did he speed up or slow down: maintained the same speed
