Bridge and man timings – find train length A train crosses a 150 m bridge in 15 s and a man (standing) in 9 s at uniform speed. What is the length of the train?

Introduction / Context:
Two timings allow solving for both the train length and speed. The man is a point obstacle (distance = train length). The bridge timing includes both train and bridge lengths.

Given Data / Assumptions:

• Bridge length = 150 m.
• t_bridge = 15 s; t_man = 9 s.
• Uniform speed.

Concept / Approach:
Let v be speed in m/s and L the train length. From man: L = v * 9. From bridge: L + 150 = v * 15. Solve the two linear equations for L.

Step-by-Step Solution:

Verification / Alternative check:
Bridge check: 225 + 150 = 375 m; at 25 m/s, time = 15 s. Man check: 225 m at 25 m/s is 9 s. Both match.

Why Other Options Are Wrong:
200 m, 135 m, 90 m: None satisfies both timing equations simultaneously.

Common Pitfalls:
Mixing which timing corresponds to which distance; remember man → distance = L, bridge → distance = L + 150.

Final Answer:
225 m