An easy question on trains and bridges for P4–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 80 m long crosses a bridge 20 m long at 10 m a second.
From the moment the front reaches the bridge until the back leaves it, how many seconds?
Show the hints (2)
💡Hint 1: Draw it: when the back leaves the bridge, how far past the bridge is the front?
💡Hint 2: The front has to travel the bridge's length plus the train's length.
Worked solution
Have a go first, then read the solution step by step.
1.When the back leaves the bridge, the front is past it by a whole train length: the front travels 20 + 80 = 100 m.
2.100 ÷ 10 = 10 seconds.
⚠️Common mistake: dividing only the bridge's length by the speed. That only brings the front to the far end, with the back not off yet; the whole train has to get off.
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