A hard question on trains and bridges for P5–P6, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P5 and P6 qualifying rounds and finals; harder ones have two trains passing, or a train wholly inside a tunnel.
The question
A train runs at a steady speed.
It crosses a bridge 122 m long: from the front reaching the bridge to the back leaving it takes 17 seconds.
Later it crosses another bridge 730 m long, and the same takes 55 seconds.
How long is the train?
Show the hints (3)
💡Hint 1: Both times the train travels bridge + train. How much further does it go the second time?
💡Hint 2: How many extra seconds do those extra 608 m take? That gives the speed.
💡Hint 3: The train travels 16 m a second; crossing the first bridge it travels 16 × 17 m.
Worked solution
Have a go first, then read the solution step by step.
1.Both times it travels bridge + train, and the train is the same, so the distances differ by 730 − 122 = 608 m and the times by 55 − 17 = 38 s.
2.The extra 608 m took 38 s: speed = 608 ÷ 38 = 16 m/s.
3.Over the first bridge the front travels 16 × 17 = 272 m, so the train is 272 − 122 = 150 m.
⚠️Common mistake: taking 122 ÷ 17 as the speed — in that time the train travels more than the bridge's length.
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