To find the average speed of the train over the entire 2 km distance, we need to use the formula for average speed:

$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$

1. Step 1: Calculate the time taken for each segment.

• For the first 1 km at 240 km/h:

$\text{Time}_1 = \frac{1 \text{ km}}{240 \text{ km/h}} = \frac{1}{240} \text{ hours}$

• For the second 1 km at 80 km/h:

$\text{Time}_2 = \frac{1 \text{ km}}{80 \text{ km/h}} = \frac{1}{80} \text{ hours}$

2. Step 2: Calculate the total time.

$\text{Total Time} = \text{Time}_1 + \text{Time}_2 = \frac{1}{240} + \frac{1}{80} \text{ hours}$

To add these fractions, find a common denominator:

$\frac{1}{240} + \frac{1}{80} = \frac{1}{240} + \frac{3}{240} = \frac{4}{240} = \frac{1}{60} \text{ hours}$

3. Step 3: Calculate the total distance.

The total distance is simply 2 km.

4. Step 4: Calculate the average speed.

$\text{Average Speed} = \frac{2 \text{ km}}{\frac{1}{60} \text{ hours}} = 2 \times 60 = 120 \text{ km/h}$

The average speed of the train is 120 km/h.

Would you like more details or have any questions?

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Here are some related questions:

1. How would the average speed change if the second segment was traveled at 100 km/h?
2. What is the average speed if the entire distance was traveled at 120 km/h?
3. How does the time of travel change if the distances were reversed?
4. How would the average speed be calculated if the distance for each speed was different?
5. What is