Problems on Trains – Bridge length from crossing time A train of length 130 m travels at 45 km/h and crosses a bridge completely in 30 seconds. What is the length of the bridge?

Introduction / Context:
Questions about trains crossing bridges test uniform speed, unit conversion, and the idea that total distance covered while clearing a bridge equals train length plus bridge length. This item reinforces the distance = speed * time model with careful unit handling.

Given Data / Assumptions:

• Train length L = 130 m.
• Speed v = 45 km/h.
• Crossing time t = 30 s.
• Assume constant speed and straight track; no acceleration phases.

Concept / Approach:
The train fully clears the bridge when its tail has just left the far end. Hence total distance D = L + B, where B is bridge length. Convert speed to m/s before using D = v * t.

Step-by-Step Solution:

Verification / Alternative check:
Reverse calculation: If bridge is 245 m, then distance to clear = 130 + 245 = 375 m. Time at 12.5 m/s is 375 / 12.5 = 30 s, which matches the given crossing time.

Why Other Options Are Wrong:
240 m: Underestimates distance; would give 370 m total and 29.6 s, not 30 s.
235 m: Yields 365 m and 29.2 s, inconsistent.
250 m: Gives 380 m and 30.4 s, too long.
None of these: Incorrect because 245 m fits perfectly.

Common Pitfalls:
Forgetting to convert km/h to m/s; using only the bridge length instead of train+bridge; or using the train length in place of the bridge length in D = v * t.

Final Answer:
245 m