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Sagot :
Sure! Let's break down the solution step-by-step based on the data provided in the table.
### Step-by-Step Solution:
#### 1. Average Speed from Hour 2 to Hour 4:
To find the average speed during a specific interval, we use the formula for average speed:
[tex]\[ \text{Average Speed} = \frac{\text{Total Distance Covered}}{\text{Total Time Taken}} \][/tex]
From hour 2 to hour 4:
- Initial distance at hour 2: [tex]\( 13.5 \)[/tex] miles
- Final distance at hour 4: [tex]\( 27.5 \)[/tex] miles
- Time interval: [tex]\(4 - 2 = 2 \)[/tex] hours
The total distance covered from hour 2 to hour 4 is:
[tex]\[ 27.5 \text{ miles} - 13.5 \text{ miles} = 14 \text{ miles} \][/tex]
So, the average speed from hour 2 to hour 4 is:
[tex]\[ \text{Average Speed} = \frac{14 \text{ miles}}{2 \text{ hours}} = 7 \text{ miles per hour} \][/tex]
#### 2. Average Speed from Hour 4 to Hour 7:
Similarly, for hour 4 to hour 7:
- Initial distance at hour 4: [tex]\( 27.5 \)[/tex] miles
- Final distance at hour 7: [tex]\( 48.5 \)[/tex] miles
- Time interval: [tex]\( 7 - 4 = 3 \)[/tex] hours
The total distance covered from hour 4 to hour 7 is:
[tex]\[ 48.5 \text{ miles} - 27.5 \text{ miles} = 21 \text{ miles} \][/tex]
So, the average speed from hour 4 to hour 7 is:
[tex]\[ \text{Average Speed} = \frac{21 \text{ miles}}{3 \text{ hours}} = 7 \text{ miles per hour} \][/tex]
#### 3. Determining if Larry Sped Up or Slowed Down:
Now, we compare the average speeds calculated for the two intervals:
- 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
Since both speeds are the same, we determine Larry did not speed up or slow down.
To summarize:
1. Average speed from hour 2 to hour 4: [tex]\( 7 \)[/tex] miles per hour
2. Average speed from hour 4 to hour 7: [tex]\( 7 \)[/tex] miles per hour
3. Larry did not speed up or slow down (consistent speed).
### Step-by-Step Solution:
#### 1. Average Speed from Hour 2 to Hour 4:
To find the average speed during a specific interval, we use the formula for average speed:
[tex]\[ \text{Average Speed} = \frac{\text{Total Distance Covered}}{\text{Total Time Taken}} \][/tex]
From hour 2 to hour 4:
- Initial distance at hour 2: [tex]\( 13.5 \)[/tex] miles
- Final distance at hour 4: [tex]\( 27.5 \)[/tex] miles
- Time interval: [tex]\(4 - 2 = 2 \)[/tex] hours
The total distance covered from hour 2 to hour 4 is:
[tex]\[ 27.5 \text{ miles} - 13.5 \text{ miles} = 14 \text{ miles} \][/tex]
So, the average speed from hour 2 to hour 4 is:
[tex]\[ \text{Average Speed} = \frac{14 \text{ miles}}{2 \text{ hours}} = 7 \text{ miles per hour} \][/tex]
#### 2. Average Speed from Hour 4 to Hour 7:
Similarly, for hour 4 to hour 7:
- Initial distance at hour 4: [tex]\( 27.5 \)[/tex] miles
- Final distance at hour 7: [tex]\( 48.5 \)[/tex] miles
- Time interval: [tex]\( 7 - 4 = 3 \)[/tex] hours
The total distance covered from hour 4 to hour 7 is:
[tex]\[ 48.5 \text{ miles} - 27.5 \text{ miles} = 21 \text{ miles} \][/tex]
So, the average speed from hour 4 to hour 7 is:
[tex]\[ \text{Average Speed} = \frac{21 \text{ miles}}{3 \text{ hours}} = 7 \text{ miles per hour} \][/tex]
#### 3. Determining if Larry Sped Up or Slowed Down:
Now, we compare the average speeds calculated for the two intervals:
- 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
Since both speeds are the same, we determine Larry did not speed up or slow down.
To summarize:
1. Average speed from hour 2 to hour 4: [tex]\( 7 \)[/tex] miles per hour
2. Average speed from hour 4 to hour 7: [tex]\( 7 \)[/tex] miles per hour
3. Larry did not speed up or slow down (consistent speed).
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