To determine the average speed of the train, we need to follow a series of steps to calculate the total distance traveled and the total time taken.
1. Calculate the distance traveled in each segment:
- For the first segment:
- Speed: [tex]\( 60 \text{ km/h} \)[/tex]
- Time: [tex]\( 0.5 \text{ hours} \)[/tex]
- Distance: [tex]\( \text{speed} \times \text{time} = 60 \times 0.5 = 30 \text{ km} \)[/tex]
- For the second segment:
- Speed: [tex]\( 30 \text{ km/h} \)[/tex]
- Time: [tex]\( 0.2 \text{ hours} \)[/tex]
- Distance: [tex]\( \text{speed} \times \text{time} = 30 \times 0.2 = 6 \text{ km} \)[/tex]
- For the third segment:
- Speed: [tex]\( 70 \text{ km/h} \)[/tex]
- Time: [tex]\( 0.7 \text{ hours} \)[/tex]
- Distance: [tex]\( \text{speed} \times \text{time} = 70 \times 0.7 = 49 \text{ km} \)[/tex]
2. Calculate the total distance traveled:
- Total distance = Distance of the first segment + Distance of the second segment + Distance of the third segment
- Total distance = [tex]\( 30 \text{ km} + 6 \text{ km} + 49 \text{ km} = 85 \text{ km} \)[/tex]
3. Calculate the total time taken:
- Total time = Time of the first segment + Time of the second segment + Time of the third segment
- Total time = [tex]\( 0.5 \text{ hours} + 0.2 \text{ hours} + 0.7 \text{ hours} = 1.4 \text{ hours} \)[/tex]
4. Calculate the average speed:
- Average speed = Total distance / Total time
- Average speed = [tex]\( 85 \text{ km} / 1.4 \text{ hours} \approx 60.71 \text{ km/h} \)[/tex]
Therefore, the average speed of the train is approximately [tex]\( 60.71 \text{ km/h} \)[/tex].
