You drive from your home to a store at 20 km/h and return by the same route at 30 km/h, ignoring the time spent in the store. What is your average speed (in km/h) for the entire round trip?

Introduction / Context:
This problem focuses on average speed for a round trip with different speeds in each direction. Even though you might be tempted to take the simple average of 20 km/h and 30 km/h, the correct method is to use the harmonic mean when distances are equal. The question evaluates whether you properly apply the total distance over total time concept.

Given Data / Assumptions:

• Speed from home to store = 20 km/h.
• Speed from store back to home = 30 km/h.
• Distance from home to store is the same as distance from store to home.
• Time spent at the store is ignored.

Concept / Approach:
Let the one way distance be d km. Time taken going is d / 20 hours and time taken coming back is d / 30 hours. The total distance is 2d and total time is d / 20 + d / 30. The average speed is then (total distance) / (total time). For equal distances, this simplifies to the harmonic mean: (2 * v1 * v2) / (v1 + v2).

Step-by-Step Solution:
Let distance one way be d km. Time going = d / 20 hours. Time returning = d / 30 hours. Total distance = 2d km. Total time = d / 20 + d / 30 = (3d + 2d) / 60 = 5d / 60 = d / 12 hours. Average speed = total distance / total time = 2d / (d / 12) = 2d * 12 / d = 24 km/h.

Verification / Alternative check:
Using harmonic mean directly: 2 * 20 * 30 / (20 + 30) = 1200 / 50 = 24 km/h. This matches the previous calculation and confirms the correctness of the result.

Why Other Options Are Wrong:

• 25 km/h and 26 km/h are close to the arithmetic mean but do not use the correct formula for average speed over equal distances.
• 22 km/h is simply an arbitrary value and does not satisfy 2d = average speed * total time when computed.

Common Pitfalls:
The most common error is to calculate (20 + 30) / 2 = 25 km/h and assume that is the correct average speed. This ignores the fact that the time spent at each speed is different. Remember that average speed depends on the total distance and total time, not just a simple mean of the speeds.

Final Answer:
The average speed for the round trip is 24 km/h.