Numerical answer
A train overtakes a man walking at 9 km/h in the same direction in 10 seconds. It crosses another man walking at 9 km/h in the opposite direction in 8 seconds. What is the length of the train, in metres?
Show answer and solution
Answer: 200
9 km/h = 9 × 5/18 = 2.5 m/s. Let the train's speed be v m/s and its length L.
- Same direction: L = (v − 2.5) × 10
- Opposite direction: L = (v + 2.5) × 8
Equating: 10v − 25 = 8v + 20 ⇒ v = 22.5 m/s (81 km/h).
L = (22.5 − 2.5) × 10 = 200 m.
Tip: Convert everything to m/s before forming equations; the relative speed is v − u when moving together and v + u when approaching.
- Same direction: L = (v − 2.5) × 10
- Opposite direction: L = (v + 2.5) × 8
Equating: 10v − 25 = 8v + 20 ⇒ v = 22.5 m/s (81 km/h).
L = (22.5 − 2.5) × 10 = 200 m.
Tip: Convert everything to m/s before forming equations; the relative speed is v − u when moving together and v + u when approaching.
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