Answer :
To find the average speed of the car traveling from city A to city B, we need to consider the entire journey.
### Step-by-Step Solution:
1. Total Distance:
- The total distance from city A to city B is 80 km.
2. Initial Distance and Speed:
- The car covers the first 30 km at a speed of 80 km/h.
3. Time for Initial Distance:
- To find the time taken to cover the first 30 km, we use the formula:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \][/tex]
- Therefore, the time taken for the initial 30 km is:
[tex]\[ \text{Time}_{\text{initial}} = \frac{30 \text{ km}}{80 \text{ km/h}} = 0.375 \text{ hours} \][/tex]
4. Remaining Distance:
- After covering the initial 30 km, the car still has:
[tex]\[ \text{Remaining distance} = 80 \text{ km} - 30 \text{ km} = 50 \text{ km} \][/tex]
5. Assumption for Remaining Speed:
- For the purposes of this problem, we'll assume that the car continues at the same speed of 80 km/h for the remaining distance.
6. Time for Remaining Distance:
- The time taken to cover the remaining 50 km is:
[tex]\[ \text{Time}_{\text{remaining}} = \frac{50 \text{ km}}{80 \text{ km/h}} = 0.625 \text{ hours} \][/tex]
7. Total Time for the Journey:
- The total time taken for the entire journey is the sum of the time taken for the initial distance and the remaining distance:
[tex]\[ \text{Total time} = \text{Time}_{\text{initial}} + \text{Time}_{\text{remaining}} = 0.375 \text{ hours} + 0.625 \text{ hours} = 1.0 \text{ hours} \][/tex]
8. Average Speed:
- Average speed is calculated using the formula:
[tex]\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{80 \text{ km}}{1.0 \text{ hours}} = 80.0 \text{ km/h} \][/tex]
### Conclusion:
- The average speed of the car over the entire journey from city A to city B is 80.0 km/h.
### Step-by-Step Solution:
1. Total Distance:
- The total distance from city A to city B is 80 km.
2. Initial Distance and Speed:
- The car covers the first 30 km at a speed of 80 km/h.
3. Time for Initial Distance:
- To find the time taken to cover the first 30 km, we use the formula:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \][/tex]
- Therefore, the time taken for the initial 30 km is:
[tex]\[ \text{Time}_{\text{initial}} = \frac{30 \text{ km}}{80 \text{ km/h}} = 0.375 \text{ hours} \][/tex]
4. Remaining Distance:
- After covering the initial 30 km, the car still has:
[tex]\[ \text{Remaining distance} = 80 \text{ km} - 30 \text{ km} = 50 \text{ km} \][/tex]
5. Assumption for Remaining Speed:
- For the purposes of this problem, we'll assume that the car continues at the same speed of 80 km/h for the remaining distance.
6. Time for Remaining Distance:
- The time taken to cover the remaining 50 km is:
[tex]\[ \text{Time}_{\text{remaining}} = \frac{50 \text{ km}}{80 \text{ km/h}} = 0.625 \text{ hours} \][/tex]
7. Total Time for the Journey:
- The total time taken for the entire journey is the sum of the time taken for the initial distance and the remaining distance:
[tex]\[ \text{Total time} = \text{Time}_{\text{initial}} + \text{Time}_{\text{remaining}} = 0.375 \text{ hours} + 0.625 \text{ hours} = 1.0 \text{ hours} \][/tex]
8. Average Speed:
- Average speed is calculated using the formula:
[tex]\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{80 \text{ km}}{1.0 \text{ hours}} = 80.0 \text{ km/h} \][/tex]
### Conclusion:
- The average speed of the car over the entire journey from city A to city B is 80.0 km/h.
