A 150 m train crosses a man walking at 6 km/h in the opposite direction in 6 seconds. What is the speed of the train (in km/h)?

Introduction / Context:
Opposite-direction crossing uses the sum of speeds as the relative speed. The train covers its entire length relative to the man in the given time, letting us compute the train's speed.

Given Data / Assumptions:

• L = 150 m.
• Man speed = 6 km/h.
• Time = 6 s.

Concept / Approach:
Relative speed v_rel = L / t = 150/6 = 25 m/s = 90 km/h. Since they move oppositely, v_rel = v_train + 6 km/h.

Step-by-Step Solution:
v_rel = 90 km/h.v_train = 90 − 6 = 84 km/h.

Verification / Alternative check:
Convert 84 km/h to m/s = 23.333...; add 6 km/h (1.666...) → 25 m/s. 25 * 6 s = 150 m.

Why Other Options Are Wrong:
66, 96, 106 km/h do not produce a 25 m/s relative speed with a 6 km/h walker.

Common Pitfalls:
Subtracting speeds (appropriate for same direction) instead of adding for opposite directions.

Final Answer:
84