A train runs 3 h at 40 km/h and then 4.5 h at 60 km/h, which totals 3/5 of its full trip distance. It wants to cover the remaining distance in 4 h. What average speed is needed for the remaining part (in km/h)?

Introduction / Context:
Segmented trips require careful accumulation of distance and then scaling to the whole. Once we find how much distance remains, the required speed for a given remaining time is just distance/time. The key is converting the “3/5 of total” into an absolute distance via the already covered kilometres.

Given Data / Assumptions:

• Stage 1: 3 h @ 40 km/h ⇒ 120 km.
• Stage 2: 4.5 h @ 60 km/h ⇒ 270 km.
• Covered so far = 390 km = 3/5 of total.
• Remaining time allowed = 4 h.

Concept / Approach:
If 390 km is 3/5, then total distance = 390 * (5/3) = 650 km. Remaining distance = 650 − 390 = 260 km. Required speed = 260/4.

Step-by-Step Solution:

Verification / Alternative check:
At 65 km/h for 4 h, the train adds 260 km, reaching the computed total of 650 km.

Why Other Options Are Wrong:
45/35 km/h would be too slow to cover 260 km in 4 h; 80 km/h is unnecessarily high.

Common Pitfalls:
Confusing 3/5 of total time with 3/5 of total distance—here it explicitly refers to distance.

Final Answer:
65 km/h