Trains • Topic 2 of 3

Crossing a Platform

A platform, bridge or tunnel has its own length, so to cross it the train must travel its own length PLUS the length of the object — measured from the moment the engine enters one end to the moment the last coach leaves the other end. So time = (train length + platform length) ÷ speed. The standard CAT pairing gives you two facts — the time to cross a pole and the time to cross a platform — at the same speed: subtract to isolate the platform’s length. If a train clears a pole in t₁ and a platform of length P in t₂ at the same speed v, then v = L/t₁ and L + P = v·t₂, so P = v(t₂ − t₁). Always keep the SAME train length in both equations; the only thing that changes between the two scenarios is the extra distance equal to the platform.

✅ Solved examples

1. A 250 m train at 90 km/h crosses a 350 m platform. How long does it take?
90 × 5/18 = 25 m/s. Distance = 250 + 350 = 600 m. Time = 600 ÷ 25 = 24 s.
2. A train 150 m long crosses a 450 m bridge in 30 s. Find its speed in km/h.
Distance = 150 + 450 = 600 m. Speed = 600 ÷ 30 = 20 m/s = 20 × 18/5 = 72 km/h.
3. A train crosses a pole in 12 s and a 200 m platform in 20 s at the same speed. Find the train’s length.
Pole: L = 12v. Platform: L + 200 = 20v. Subtract: 200 = 8v ⇒ v = 25 m/s. Then L = 12 × 25 = 300 m.
4. A 400 m train at 60 km/h enters a 1.1 km tunnel. How long until the whole train has cleared the tunnel?
60 × 5/18 = 50/3 m/s. Distance = 400 + 1100 = 1500 m. Time = 1500 ÷ (50/3) = 1500 × 3/50 = 90 s.

✏️ Practice — try these, take hints as needed

1. A 200 m train at 72 km/h crosses a 400 m platform in how many seconds?
72 km/h = 20 m/s.
Distance = 200 + 400.
600 ÷ 20.
30 s
2. A 180 m train crosses a 270 m bridge in 18 s. Speed in km/h?
Distance = 180 + 270 = 450 m.
Speed = 450 ÷ 18 = 25 m/s.
25 × 18/5.
90 km/h
3. A train crosses a pole in 8 s and a 240 m platform in 20 s at the same speed. Train length?
L = 8v and L + 240 = 20v.
Subtract: 240 = 12v.
v = 20 m/s, then L = 8 × 20.
160 m
4. A 300 m train at 54 km/h crosses a 450 m platform. Time taken?
54 km/h = 15 m/s.
Distance = 750 m.
750 ÷ 15.
50 s
5. A train 220 m long passes a platform of equal length in 22 s. Find its speed in km/h.
Distance = 220 + 220 = 440 m.
Speed = 440 ÷ 22 = 20 m/s.
20 × 18/5.
72 km/h

📝 Topic test — 8 questions

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