Laxman must cover 6 km in 45 minutes (0.75 h). He covers the first half of the distance (3 km) in two-thirds of the total time (30 minutes). What speed (in km/h) is required to cover the remaining 3 km in the remaining 15 minutes?

Introduction / Context:
This question checks understanding of time partitioning and speed requirements when part of a journey uses a disproportionate share of the total time. The key is to compute remaining time and distance, then apply speed = distance / time.

Given Data / Assumptions:

• Total distance = 6 km; total time = 45 minutes.
• First half (3 km) takes 2/3 of total time = 30 minutes.
• Remaining half = 3 km; remaining time = 15 minutes.

Concept / Approach:
For the leftover segment, convert minutes to hours and compute the constant speed needed to finish on time.

Step-by-Step Solution:

Verification / Alternative check:
Check total: First 3 km use 30 minutes; last 3 km at 12 km/h uses 15 minutes; total 45 minutes as required.

Why Other Options Are Wrong:

• 16 km/h and 8 km/h: Over- or under-estimate the needed pace for 3 km in 15 minutes.
• 3 km/h and 10 km/h: Do not meet the 15-minute remainder constraint.

Common Pitfalls:
Forgetting to convert minutes to hours, or misallocating the remaining time.

Final Answer:
12 km/h