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
Trains A and B run towards each other on parallel tracks at steady speeds.
A is 60 m long and travels 16 m a second;
B is 64 m long.
From the moment their fronts meet until their backs part takes 4 seconds.
How many metres a second does train B travel?
Show the hints (3)
💡Hint 1: From fronts meeting to backs parting, how far do the two trains travel between them? Draw it.
💡Hint 2: How far do they travel between them each second?
💡Hint 3: Together they travel 124 m, so 124 ÷ 4 m a second, of which 16 m is train A.
Worked solution
Have a go first, then read the solution step by step.
1.From fronts meeting to backs parting, the fronts of A and B travel both lengths between them: 60 + 64 = 124 m.
2.Each second they cover 124 ÷ 4 = 31 m together.
3.Train B: 31 − 16 = 15 m a second.
⚠️Common mistake: using only one train's length. Each train has to get completely past the other.
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