Calculation of Average Speed:

To calculate the average speed of the train for the entire journey, we need to consider the individual distances covered at different speeds and the total time taken for the journey.

Step 1: Calculate the distances covered:

Let's assume the total distance of the journey is 'D'. Since the train covers half of the journey at a speed of 30 m/s, the distance covered at this speed is D/2. Similarly, the distance covered at a speed of 40 m/s is also D/2.

Step 2: Calculate the time taken:

To find the time taken, we can use the formula: time = distance/speed.

For the first half of the journey, the time taken is (D/2) / 30 = D/60 seconds.
For the second half of the journey, the time taken is (D/2) / 40 = D/80 seconds.

Step 3: Calculate the total time:

The total time taken for the entire journey is the sum of the times taken for each half of the journey.
Total time = D/60 + D/80 = (4D + 3D) / 240 = 7D / 240 seconds.

Step 4: Calculate the average speed:

The average speed is given by the formula: average speed = total distance / total time.

The total distance is D.
The total time is 7D / 240 seconds.

Therefore, the average speed is D / (7D / 240) = 240/7 m/s.

Explanation:

The average speed of the train for the entire journey is found by considering the distances covered at different speeds and the time taken for each half of the journey. The average speed is calculated by dividing the total distance by the total time.

In this case, since the train covers half of the journey at a speed of 30 m/s and the other half at a speed of 40 m/s, the average speed is found to be 240/7 m/s.

It's important to note that the average speed is not simply the arithmetic mean of the individual speeds. Instead, it is determined by considering the distances covered and the time taken at each speed.