A train of length 200 meters crosses a man running at 10 km/hr in the same…

Concept: When two bodies move in the same direction, their relative speed equals the difference of their individual speeds (Relative Speed = Faster Speed − Slower Speed). When a body of a known length crosses another moving body, the relative speed between them equals the length of the first body divided by the time taken to cross it (Relative Speed = Length ÷ Time). Speeds convert between m/s and km/hr by multiplying by 18/5.

1. Find the relative speed from the crossing: Relative Speed = Length of train ÷ Time taken = 200 m ÷ 10 s = 20 m/s.

2. Convert this relative speed to km/hr: 20 m/s × 18/5 = 72 km/hr.

3. Since the train and the man move in the same direction, Relative Speed = Train Speed − Man's Speed, so Train Speed = Relative Speed + Man's Speed = 72 + 10 = 82 km/hr.

Cross-check: At 82 km/hr, the relative speed with respect to the man is 82 − 10 = 72 km/hr, i.e. 20 m/s. Crossing a 200 m train at 20 m/s takes 200 ÷ 20 = 10 seconds, matching the time given in the question.