To calculate the average speed of the train on its entire journey, we can use the concept of harmonic mean. The harmonic mean of two speeds is used when the distances covered are the same.
Let's denote the distance between Bombay and Pune as 'D'.
On the onward journey, the train covers the distance 'D' with an average speed of 100 km/h. Therefore, the time taken for the onward journey is D/100 hours.
On the return journey, the train covers the same distance 'D' with an average speed of 50 km/h. Hence, the time taken for the return journey is D/50 hours.
The total time taken for the entire journey is the sum of the times taken for the onward and return journeys:
Total time = D/100 + D/50 = (2D + D)/100 = 3D/100
To find the average speed, we divide the total distance (2D) by the total time (3D/100):
Average speed = Total distance / Total time = 2D / (3D/100) = 200/3 km/h ≈ 66.67 km/h
Therefore, the average speed of the Deccan Queen train on its entire journey from Bombay to Pune and back is approximately 66.67 km/h.