Introduction
"Problems on Trains" is Time-Speed-Distance (Chapter 15) with one key addition: the length of the
train itself must be treated as part of the distance travelled when crossing something.
Core Rule — What Counts as "Distance"
| Train Crosses... | Distance Covered |
|---|
| A stationary point/pole/man | Length of the train |
| A platform/bridge of length L | Length of the train + L |
| Another train (opposite direction) | Sum of both train lengths; relative speed = sum of speeds |
| Another train (same direction) | Sum of both train lengths; relative speed = difference of speeds |
Q. A train 150 m long is running at 54 km/h. Find the time it takes to cross a pole.
Speed = 54 × 5/18 = 15 m/s
Time = Distance/Speed = 150/15 = 10 seconds
Q. A train 200 m long crosses a platform 300 m long in 25 seconds. Find the speed of the train in km/h.
Total distance = 200+300 = 500 m
Speed = 500/25 = 20 m/s = 20 × 18/5 = 72 km/h
Two Trains Crossing Each Other
Flowchart — Two Trains Crossing
Total Distance = Length of Train A + Length of Train B
↓
Opposite directions → Relative Speed = v₁ + v₂
Same direction → Relative Speed = v₁ − v₂
↓
Time = Total Distance / Relative Speed
Q. Two trains 120 m and 180 m long run at 54 km/h and 36 km/h respectively in opposite directions on parallel tracks. Find the time they take to cross each other.
Relative speed = 54+36 = 90 km/h = 90×5/18 = 25 m/s
Total distance = 120+180 = 300 m
Time = 300/25 = 12 seconds
Train Crossing a Moving Person/Object
Q. A train 100 m long is running at 40 km/h. Find the time it takes to cross a man running at 4 km/h in the direction opposite to the train.
Relative speed = 40+4 = 44 km/h = 44×5/18 = 220/18 m/s ≈ 12.22 m/s
Time = 100/12.22 ≈ 8.2 seconds
💡 Exam Tip: Always ask two questions first: (1) "What total length must be covered?" (train length alone, or plus platform, or plus another train) and (2) "What's the relative speed?" (same direction = subtract, opposite = add). Answering these correctly solves 90% of train problems instantly.
✅ Practice Focus: Distance rules for pole/platform/another train · Relative speed for same vs opposite direction · Two-trains-crossing formula · Train crossing a moving person (treat person's speed like a second train).