Question
A train 200 m long crosses a platform 300 m long in 25 seconds. Find the speed of the train. If another train of length 150 m approaches from the opposite direction at 72 km/h, how long will they take to cross each other?
(CBSE 7 & 8 pattern)
Solution — Step by Step
When a train crosses a platform, the total distance covered = train length + platform length.
When two objects move toward each other, their relative speed = sum of speeds.
Train 1: km/h m/s
Train 2: km/h m/s
Total distance to cross each other = sum of both train lengths:
Why This Works
The fundamental relationship is . For crossing problems, we need to figure out the correct distance (what exactly needs to pass what) and the correct speed (actual or relative).
graph TD
A["TSD Problem"] --> B{"What's crossing what?"}
B -->|"Train crosses a pole/person"| C["Distance = train length"]
B -->|"Train crosses a platform/bridge"| D["Distance = train + platform"]
B -->|"Two trains crossing"| E["Distance = sum of lengths"]
E --> F{"Direction?"}
F -->|"Opposite"| G["Relative speed = v₁ + v₂"]
F -->|"Same direction"| H["Relative speed = |v₁ - v₂|"]
A --> I{"Average speed?"}
I --> J["avg speed = total distance<br/>÷ total time<br/>(NOT average of speeds!)"]Alternative Method — Unit Conversion Shortcut
To convert km/h to m/s: multiply by .
To convert m/s to km/h: multiply by .
For the train problem, you can work entirely in km/h or entirely in m/s — just be consistent.
Average speed is NOT the average of two speeds. If you travel 60 km at 30 km/h and 60 km at 60 km/h, the average speed = km/h, not km/h. Use total distance divided by total time, always.
Common Mistake
When two trains move in the same direction, students add their speeds instead of subtracting. If both go in the same direction, the faster one approaches the slower one at a relative speed of . Adding gives the relative speed for opposite directions only. This changes the answer dramatically — getting it wrong can double or halve your time.