To solve this problem, we need to find Larry's average speed during two time intervals: from hour 2 to hour 4, and from hour 4 to hour 7. We will then compare these speeds to determine if Larry sped up, slowed down, or maintained the same speed.
Step 1: Determine Larry's average speed from hour 2 to hour 4
Firstly, let's find the time interval from hour 2 to hour 4:
[tex]\[
\text{Time interval from hour 2 to hour 4} = 4 - 2 = 2 \text{ hours}
\][/tex]
Next, find the distance covered during this time interval:
[tex]\[
\text{Distance traveled from hour 2 to hour 4} = 27.5 \, \text{mi} - 13.5 \, \text{mi} = 14 \, \text{mi}
\][/tex]
Now, calculate the average speed over this interval:
[tex]\[
\text{Average speed from hour 2 to hour 4} = \frac{\text{Distance}}{\text{Time}} = \frac{14 \, \text{mi}}{2 \, \text{hr}} = 7 \, \text{mi/hr}
\][/tex]
Step 2: Determine Larry's average speed from hour 4 to hour 7
Next, let's find the time interval from hour 4 to hour 7:
[tex]\[
\text{Time interval from hour 4 to hour 7} = 7 - 4 = 3 \text{ hours}
\][/tex]
Next, find the distance covered during this time interval:
[tex]\[
\text{Distance traveled from hour 4 to hour 7} = 48.5 \, \text{mi} - 27.5 \, \text{mi} = 21 \, \text{mi}
\][/tex]
Now, calculate the average speed over this interval:
[tex]\[
\text{Average speed from hour 4 to hour 7} = \frac{\text{Distance}}{\text{Time}} = \frac{21 \, \text{mi}}{3 \, \text{hr}} = 7 \, \text{mi/hr}
\][/tex]
Step 3: Determine if Larry sped up or slowed down
Compare the average speeds during the two intervals:
- From hour 2 to hour 4, the average speed was [tex]\(7 \, \text{mi/hr}\)[/tex].
- From hour 4 to hour 7, the average speed was also [tex]\(7 \, \text{mi/hr}\)[/tex].
Since the average speeds are the same, Larry maintained the same speed during both intervals.
Hence, the final answers are:
- Average speed from hour 2 to hour 4: [tex]\(7 \, \text{mi/hr}\)[/tex]
- Average speed from hour 4 to hour 7: [tex]\(7 \, \text{mi/hr}\)[/tex]
- Larry maintained the same speed.
