Time and Distance – Finish a target journey with time already spent: A bullock cart must cover 80 km in 10 hours. It completes half the journey in 3/5 of the total time. What speed is required for the remaining half to finish on time?

Introduction / Context:
This is a remaining-time problem. After a portion of the journey consumes a specified fraction of the total time, we compute the leftover time and required speed to complete the rest of the distance on schedule.

Given Data / Assumptions:

• Total distance = 80 km; total time = 10 h.
• Half the distance (40 km) is done in 3/5 of total time = 6 h.
• Remaining distance = 40 km; remaining time = 4 h.

Concept / Approach:
Required speed for the remainder = remaining distance / remaining time.

Step-by-Step Solution:
Remaining speed = 40 km / 4 h = 10 km/h.

Verification / Alternative check:
First half average = 40/6 ≈ 6.67 km/h; second half at 10 km/h yields total average 80/10 = 8 km/h, which meets the schedule.

Why Other Options Are Wrong:
Speeds other than 10 km/h miss the 4-hour remainder constraint for the remaining 40 km.

Common Pitfalls:
Halving time instead of distance or confusing 3/5 of time with 3/5 of distance.

Final Answer:
10 km/h