A man walks 7.5 km at 3 km/h. What speed must he maintain for the next 2 hours so that his overall average speed for the whole session is 4 km/h?

Introduction / Context:
Average speed = total distance / total time. Compute required remaining distance to hit the target average over the total duration, then divide by the remaining time to get the needed speed for the second segment.

Given Data / Assumptions:

• First segment: 7.5 km at 3 km/h ⇒ 2.5 h.
• Second segment duration: 2 h at unknown speed v.
• Target average = 4 km/h over total 4.5 h.

Concept / Approach:
Total distance needed = 4 * 4.5 = 18 km. Remaining distance = 18 − 7.5 = 10.5 km. Required v = 10.5 / 2.

Step-by-Step Solution:

Verification / Alternative check:
Total distance = 7.5 + 10.5 = 18 km; time = 2.5 + 2 = 4.5 h; average = 18/4.5 = 4 km/h.

Why Other Options Are Wrong:
3.65/4.75/6.50 km/h would not produce the exact 18 km total in 4.5 h.

Common Pitfalls:
Using average of speeds instead of weighted-average based on time and distance.

Final Answer:
5.25 km/h