A cart must cover 80 km in 10 hours. It covers half the distance in 3/5 of the total time. What speed is needed to cover the remaining distance in the time left?

Introduction / Context:
This is a two-phase motion problem with a fixed total time. Once part of the journey is completed, compute the remaining time and the speed required to finish on schedule.

Given Data / Assumptions:

• Total distance = 80 km; total time = 10 h.
• First 40 km (half the distance) is covered in (3/5)*10 = 6 h.
• Remaining distance = 40 km; remaining time = 4 h.

Concept / Approach:
Required speed for the second part equals remaining distance divided by remaining time.

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

Verification / Alternative check:
Average speed overall = 80/10 = 8 km/h; doing 40 km in 6 h implies average 6.67 km/h for the first half, making 10 km/h necessary for the second half to meet the average.

Why Other Options Are Wrong:
8 km/h maintains the overall average but does not finish in time given the slow first half; 20 km/h and 6.4 km/h misapply the time split.

Common Pitfalls:
Using the target average speed (8 km/h) for the remainder despite the earlier 6 h already spent on half the distance.

Final Answer:
10 km/h