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 84 m long runs at a steady speed.
Passing a lamp post beside the track, from front reaching the post to back passing it, takes 7 seconds.
Later, at the same speed, it crosses a bridge 144 m long.
From the front reaching the bridge until the back leaves it, how many seconds?
Show the hints (2)
💡Hint 1: Use the lamp post first to find the train's speed.
💡Hint 2: To cross the bridge, how far does the train travel?
Worked solution
Have a go first, then read the solution step by step.
1.Passing the post it travels one train length, 84 m, in 7 s: speed = 84 ÷ 7 = 12 m/s.
2.Crossing the bridge it travels bridge 144 + train 84 = 228 m.
3.228 ÷ 12 = 19 seconds.
⚠️Common mistake: working out 144 ÷ 12. At that point the back is not off yet: the train's length is left out.
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