Explanation:
To solve this problem, we need to use the formula for average speed which is:

Average speed = Total distance traveled / Total time taken

Let's assume that the total distance between the two stations is D km.

Step 1: Calculate the distance covered in the first half of the journey

Distance covered in the first half of the journey = D/2 km

Step 2: Calculate the time taken to cover the first half of the journey

Time taken to cover the first half of the journey = Distance covered / Speed

= (D/2) / 40 km/h

= (D/2) x (1/40) h

= D/80 h

Step 3: Calculate the distance covered in the second half of the journey

Distance covered in the second half of the journey = D/2 km

Step 4: Calculate the time taken to cover the second half of the journey

Time taken to cover the second half of the journey = Distance covered / Speed

= (D/2) / 60 km/h

= (D/2) x (1/60) h

= D/120 h

Step 5: Calculate the total time taken for the journey

Total time taken for the journey = Time taken for the first half + Time taken for the second half

= D/80 + D/120 h

= (3D + 2D) / 240 h

= 5D / 240 h

Step 6: Calculate the average speed for the journey

Average speed = Total distance traveled / Total time taken

= D / (5D/240)

= 240/5 km/h

= 48 km/h

Therefore, the average speed of the train for the entire journey is 48 km/h.

Average speed= total distance/ total time

let the total distance covered be x

then for the first X/2 distance, time taken will be= distance/ speed= X/(2*40)

for the next X/2 distance, time=X/(2*60)

hence, total time= X/80 + X/120= 5x/240=X/48 hours( because units are given in km/h)

hence average speed= X/(X/48)= 48 km/ h