A train of length 180 meters is running at a speed of 72 km/h. How much time will it take to cross a bridge 350 meters long?

Question

A train of length 180 meters is running at a speed of 72 km/h. How much time will it take to cross a bridge 350 meters long?

1. A. 26.5 seconds (Correct answer)
2. B. 24.5 seconds
3. C. 23.5 seconds
4. D. 27.5 seconds

Correct Answer

Option A — 26.5 seconds

Detailed Solution & Explanation

The correct answer is 26.5 seconds.

Shortcut Trick

• To cross a bridge, a train must travel its own length plus the bridge's length.
• Total distance $= 180 + 350 = 530$ m.
• Convert speed: $72 \text{ km/h} \times \dfrac{5}{18} = 20$ m/s.
• Time $= \dfrac{530}{20} = \textbf{26.5}$ seconds.

Alternate Method

• Working in kilometres and hours: distance $= 0.53$ km, speed $= 72$ km/h.
• Time $= \dfrac{0.53}{72}$ h $= 0.0073\overline{6}$ h $\times 3600 = \textbf{26.5}$ s.
• The metre-second route is faster, which is why the $\frac{5}{18}$ conversion is worth memorising.

Additional Information

• The distance depends on what is being crossed:
  • a pole, post or man — the train covers only its own length (the object has no length);
  • a platform, bridge or tunnel — train length + object length.
• Conversions: km/h → m/s multiply by $\dfrac{5}{18}$; m/s → km/h multiply by $\dfrac{18}{5}$.
• For two trains, use relative speed: add the speeds when moving in opposite directions, subtract when moving in the same direction.