A car completes a journey in 8 hours, covering half the distance at 40 km/h and the remaining half at 60 km/h. What is the total length of the journey (in km)?

Introduction / Context:
When half the distance is covered at one speed and half at another, the overall average speed for the full trip is the harmonic mean of the two speeds (not the arithmetic mean).

Given Data / Assumptions:

• First half at 40 km/h, second half at 60 km/h.
• Total time for the whole distance = 8 hours.

Concept / Approach:
For equal halves by distance, average speed V = 2 / (1/40 + 1/60) = 48 km/h. Distance D = V * total time.

Step-by-Step Solution:

Verification / Alternative check:
Let distance be 2x. Times: x/40 + x/60 = 8 → x(1/40 + 1/60) = 8 → x/24 = 8 → x = 192 → D = 384 km.

Why Other Options Are Wrong:
Values like 400 or 420 km correspond to using an incorrect average (e.g., arithmetic mean) or miscomputing time fractions.

Common Pitfalls:
Averaging speeds arithmetically for equal distance halves; always use total-distance over total-time logic.

Final Answer:
384 km