A traveler covers three equal legs of 39 km each at 26 km/h, 39 km/h, and 52 km/h respectively. What is the average speed for the entire 117 km journey?

Introduction / Context:
When multiple legs cover equal distances at different speeds, the overall average speed must be computed from total distance divided by total time; it is not the simple average of the speeds.

Given Data / Assumptions:

• Leg distances: 39 km each (total 117 km).
• Speeds: 26 km/h, 39 km/h, 52 km/h.
• Constant speeds per leg; negligible stops.

Concept / Approach:
Total time is the sum of leg times: t = 39/26 + 39/39 + 39/52 hours. Average speed = total distance / total time.

Step-by-Step Solution:
Compute times: 39/26 = 1.5 h; 39/39 = 1 h; 39/52 = 0.75 h.Total time = 1.5 + 1 + 0.75 = 3.25 h.Total distance = 39 + 39 + 39 = 117 km.Average speed = 117 / 3.25 = 36 km/h.

Verification / Alternative check:
Multiply 36 km/h by 3.25 h: 36*3 = 108; 36*0.25 = 9; total 117 km, matching the distance.

Why Other Options Are Wrong:
33 and 34 km/h underestimate the pace; 38 km/h is too high given the time spent at 26 km/h on one full leg.

Common Pitfalls:
Averaging the three speeds arithmetically, which ignores varying times per leg.

Final Answer:
36 km/h