Numerical aptitude · Time and motion
Trains, made easy
💡 The idea
A train has length. To pass something, its front must travel its whole length (plus the length of what it passes).
🚆 passes a pole
distance = train→🚆 passes a platform
= train + platform→🚆🚆 pass each other
= train 1 + train 2
distance = train→🚆 passes a platform
= train + platform→🚆🚆 pass each other
= train 1 + train 2
🧭 The method: 3 steps
- Change the speed to m/s (× 5/18).
- Find the distance: train length (+ platform or other train).
- Time = distance ÷ speed. Two trains: add speeds if opposite, subtract if same way.
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
Loading the pictures…
✏️ Worked examples
Example 1. A 150 m train at 54 km/h passes a pole. Time?
- 54 × 5/18 = 15 m/s
- Distance = 150 m
- Time = 150 ÷ 15 = 10 seconds
Example 2. Same train passes a 300 m platform. Time?
- Distance = 150 + 300 = 450 m
- Time = 450 ÷ 15 = 30 seconds
Example 3. Trains of 100 m and 150 m at 54 and 36 km/h, towards each other. Time to pass?
- Relative speed = 54 + 36 = 90 km/h = 25 m/s
- Distance = 100 + 150 = 250 m
- Time = 250 ÷ 25 = 10 seconds
⚠️ Where people go wrong
- Forgetting the train’s own length when it passes a platform.
- Not changing km/h into m/s.
- Same direction → subtract the speeds.
📌 Remember
- Pole: L ÷ S
- Platform: (L + P) ÷ S
- Two trains: (L1 + L2) ÷ (S1 ± S2)