Average speed over unequal segments A man covers the first 30 km at 6 km/h and the remaining 40 km in 5 hours. What is his average speed for the 70 km journey?

Introduction / Context:
Average speed over multiple legs equals total distance divided by total time, not the average of individual speeds. When legs have different durations, using total distance / total time ensures correct weighting.

Given Data / Assumptions:

• Leg 1: 30 km at 6 km/h.
• Leg 2: 40 km in 5 h (so the speed on leg 2 is 8 km/h).
• Total distance = 70 km.

Concept / Approach:
Compute time per leg, sum to total time, then divide total distance by total time.

Step-by-Step Solution:

Verification / Alternative check:
Weighted-by-time average of speeds: (6 for 5 h and 8 for 5 h) ⇒ (6*5 + 8*5) / (5+5) = 70/10 = 7.

Why Other Options Are Wrong:
8 km/h uses the last leg speed; 64/11 ≈ 5.82 and 7.5 km/h mis-handle weighting.

Common Pitfalls:
Taking the arithmetic mean (6+8)/2 = 7 (which coincidentally equals the correct value only because the times are equal here; in general you must use total distance / total time).

Final Answer:
7 km/h