Average speed for a round trip: Einstein travels from Ahmedabad to Lucknow at 40 km/h and returns at 60 km/h. What is the overall average speed for the entire journey (same distance each way)?

Introduction / Context:
Average speed over a round trip with unequal speeds each way is a classic aptitude topic. Because the distances are equal, the correct average is not the simple arithmetic mean. Instead, we must use the harmonic mean of the two speeds to capture time properly.

Given Data / Assumptions:

• Outbound speed = 40 km/h
• Return speed = 60 km/h
• Distances in both directions are equal

Concept / Approach:
The average speed for equal distances is 2ab/(a + b). This comes from total distance divided by total time, where time for each leg is distance/speed. Using a and b for the two speeds ensures the formula accounts for slower segments contributing more time.

Step-by-Step Solution:

Verification / Alternative check:
Assume a 60 km one way trip. Time out = 60/40 = 1.5 h. Time back = 60/60 = 1 h. Total distance = 120 km. Total time = 2.5 h. 120/2.5 = 48 km/h.

Why Other Options Are Wrong:

• 50, 52, 56 km/h: arithmetic style guesses that ignore time weighting.
• 45 km/h: underestimates by overweighting the slower leg incorrectly.

Common Pitfalls:
Using (40 + 60)/2 = 50 is a common error. The arithmetic mean applies when times are equal, not distances.

Final Answer:
48 km/h