Average speed for a round trip: A ship sails to a mark at 15 km/h and returns at 10 km/h over the same distance. What is the average speed for the whole journey?

Introduction / Context:
Average speed for equal distance out and back uses the harmonic mean, not the arithmetic mean.

Given Data / Assumptions:

• Outbound speed = 15 km/h
• Return speed = 10 km/h

Concept / Approach:
For equal distances, average speed = 2*x*y/(x + y).

Step-by-Step Solution:

Verification / Alternative check:
Pick a distance such as 30 km each way. Time = 30/15 + 30/10 = 2 + 3 = 5 h. Total distance = 60 km. 60/5 = 12 km/h.

Why Other Options Are Wrong:

• 5 km/h and 25 km/h: Far from the harmonic mean.
• 12.5 km/h: Arithmetic mean trap, not correct for round trips.

Common Pitfalls:
Using the arithmetic mean of speeds instead of the harmonic mean for equal distances.

Final Answer: