A medium question on trains and bridges for P5, 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 travelling at 10 m a second crosses a bridge 100 m long.
From the front reaching the bridge to the back leaving it takes 18 seconds.
How long is the train?
Show the hints (2)
💡Hint 1: How far does the train travel in those 18 seconds?
💡Hint 2: That distance is made of which two parts?
Worked solution
Have a go first, then read the solution step by step.
1.In 18 seconds the front travels 10 × 18 = 180 m.
2.Distance = bridge + train, so the train is 180 − 100 = 80 m.
⚠️Common mistake: taking the distance travelled to be just the bridge, 100 m.
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