Average speed for equal distances: A car goes from A to B at 42 km/h and returns from B to A at 48 km/h. Find the overall average speed for the round trip (equal distances each way).

Introduction / Context:
For a round trip over equal distances with different speeds, the overall average speed is the harmonic mean of the two speeds, not the arithmetic mean. This accounts for the greater time spent at the slower speed.

Given Data / Assumptions:

• Outbound speed = 42 km/h
• Return speed = 48 km/h
• Equal distances each way

Concept / Approach:
Average speed for equal distances = 2ab / (a + b). This is derived from total distance divided by total time: time = d/a + d/b; distance = 2d.

Step-by-Step Solution:

Verification / Alternative check:
Assume 90 km each way: time = 90/42 + 90/48 = 2.142857… + 1.875 = 4.017857… h. Total distance = 180 km → 180 / 4.017857… ≈ 44.8 km/h.

Why Other Options Are Wrong:

• 45.0, 44.0, 46.0, 48.0: approximations or arithmetic means that ignore correct time weighting.

Common Pitfalls:
Using the arithmetic mean (42 + 48)/2 = 45, which is incorrect for equal distances at different speeds.

Final Answer:
44.8 km/h