To determine Larry's average speed over different intervals and whether his speed changed, we'll analyze the provided data step-by-step.
### Step 1: Calculate the Average Speed from Hour 2 to Hour 4
1. Identify the Time Interval:
- Starting time: 2 hours
- Ending time: 4 hours
- Time difference: [tex]\( 4 - 2 = 2 \)[/tex] hours
2. Identify the Distance Covered:
- Starting distance: 13.5 miles
- Ending distance: 27.5 miles
- Distance difference: [tex]\( 27.5 - 13.5 = 14 \)[/tex] miles
3. Calculate the Average Speed:
- Average speed: [tex]\( \frac{\text{Distance difference}}{\text{Time difference}} = \frac{14 \text{ miles}}{2 \text{ hours}} = 7 \text{ miles/hour} \)[/tex]
So, Larry's average speed from hour 2 to hour 4 is [tex]\( \boxed{7} \)[/tex] miles per hour.
### Step 2: Calculate the Average Speed from Hour 4 to Hour 7
1. Identify the Time Interval:
- Starting time: 4 hours
- Ending time: 7 hours
- Time difference: [tex]\( 7 - 4 = 3 \)[/tex] hours
2. Identify the Distance Covered:
- Starting distance: 27.5 miles
- Ending distance: 48.5 miles
- Distance difference: [tex]\( 48.5 - 27.5 = 21 \)[/tex] miles
3. Calculate the Average Speed:
- Average speed: [tex]\( \frac{\text{Distance difference}}{\text{Time difference}} = \frac{21 \text{ miles}}{3 \text{ hours}} = 7 \text{ miles/hour} \)[/tex]
So, Larry's average speed from hour 4 to hour 7 is [tex]\( \boxed{7} \)[/tex] miles per hour.
### Step 3: Determine If Larry Sped Up or Slowed Down
1. Compare the Average Speeds:
- Average speed from hour 2 to hour 4: 7 miles/hour
- Average speed from hour 4 to hour 7: 7 miles/hour
2. Analyze the Speed Change:
- Since the average speed is the same for both intervals, Larry maintained the same speed.
So, Larry [tex]\( \boxed{\text{maintained the same speed}} \)[/tex].
In summary:
- Average speed from hour 2 to hour 4: [tex]\( 7 \)[/tex] miles per hour
- Average speed from hour 4 to hour 7: [tex]\( 7 \)[/tex] miles per hour
- Larry maintained the same speed.
