Olympiad topic · P4–P6
Trains and bridges
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.
Try one
★★ MediumA 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?
- 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?
- 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.
Answer: 19 seconds
Four levels, step by step
- ★EasyFree2 question types · unlimited questionsA bridge, a lamp post.
- ★★MediumFree2 question types · unlimited questionsThe train's length from the time.
- ★★★HardFree3 question types · unlimited questionsTwo trains passing, two bridges compared.
- ★★★★Expert (competition level)VIP3 question types · unlimited questionsThe time wholly inside a tunnel, passing people on foot, two trains both ways.
Trains and bridges: what it is and how to solve it
A train has length: find the time, its length or its speed as it passes a bridge, a tunnel or another train.
For example: A 90 m train at 25 m a second crosses a 260 m bridge. From its front reaching the bridge to its back leaving it? (260 + 90) ÷ 25 = 14 seconds.
The key idea: From front on to back off, the train travels bridge + train length. When two trains pass, the distance is both lengths together, at the sum or difference of their speeds.
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