A bus covers a certain journey in 16 hours, traveling half the distance at 40 km/h and the other half at 60 km/h. Find the total length of the journey (in km).

Introduction / Context:
When equal distances are traveled at two different speeds, average speed for the whole trip is the harmonic mean of the two speeds. Multiplying that average by total time gives the total distance.

Given Data / Assumptions:

• Half the distance at 40 km/h; half at 60 km/h.
• Total time = 16 h.

Concept / Approach:
Average speed for equal-distance halves: V = 2 / (1/40 + 1/60) = 48 km/h. Then Distance = V × Time.

Step-by-Step Solution:

Verification / Alternative check:
Let total distance be 2x. Time = x/40 + x/60 = x/24. Given total time 16 = x/24 ⇒ x = 384 ⇒ distance = 768 km.

Why Other Options Are Wrong:
Other values arise from using the arithmetic mean of speeds or misworking the time equation.

Common Pitfalls:
Averaging speeds directly for equal distances; not distinguishing equal “distance” vs equal “time.”

Final Answer:
768 km