A train overtakes two people walking in the same direction at 2 km/h and 4 km/h and passes them completely in 9 s and 10 s, respectively. What is the length of the train?

Introduction / Context:
With both pedestrians moving in the same direction as the train, the relative speeds are (V − 2) and (V − 4) km/h, respectively. The train covers its own length relative to each in the given times. Equating the two expressions solves for V and then length.

Given Data / Assumptions:

• Times = 9 s (against 2 km/h) and 10 s (against 4 km/h).
• Train speed = V km/h; train length = L m.

Concept / Approach:
L = relative_speed * time. In m/s, relative speed against each walker is ((V − w) * 1000/3600). Set L from both situations equal to solve for V.

Step-by-Step Solution:
((V − 2)*1000/3600)*9 = ((V − 4)*1000/3600)*10 → 9(V − 2) = 10(V − 4).9V − 18 = 10V − 40 → V = 22 km/h.Relative speed vs 2 km/h = 20 km/h = 5.555... m/s; L = 5.555... * 9 ≈ 50 m.

Verification / Alternative check:
Against 4 km/h: relative 18 km/h = 5 m/s; 5 * 10 s = 50 m, consistent.

Why Other Options Are Wrong:
45, 54, 72 m correspond to using incorrect relative speeds or mixing km/h and m/s.

Common Pitfalls:
Not converting units consistently or forgetting that the train covers its full length relative to the walker.

Final Answer:
50 meters