Introduction
Problems about trains passing a pole or a platform are extremely common in Time, Speed & Distance. They test understanding of what distance the train actually needs to cover and require consistent unit conversion (km/h ↔ m/s) when time is in seconds.
This pattern is important because it combines length, speed and time - and once you know the exact distance to be covered (train length vs. train + platform length) the rest is mechanical.
Pattern: Trains Passing Pole / Platform
Pattern
Key concept: Time = Distance to be covered ÷ Speed (use consistent units).
- Passing a pole or a stationary point: Distance = length of the train.
- Passing a platform (standing length L_p): Distance = train length + platform length.
- When two trains pass each other: If opposite directions → add speeds; if same direction → subtract speeds. Distance = sum of their lengths.
- Units: If time in seconds and lengths in metres, convert speed from km/h → m/s using ×5/18 (or divide by 3.6 when converting m/s → km/h).
Step-by-Step Example
Question
A train 150 m long runs at 72 km/h. How long will it take to pass a pole?
Solution
-
Step 1: Identify given values
Train length = 150 m; speed = 72 km/h; passing a pole → distance to cover = train length = 150 m. -
Step 2: Convert speed to m/s (since distance in metres and time asked in seconds)
72 km/h × (5/18) = 72 × 5 ÷ 18 = 20 m/s. -
Step 3: Apply Time = Distance ÷ Speed
Time = 150 ÷ 20 = 7.5 seconds. -
Final Answer:
The train will pass the pole in 7.5 s. -
Quick Check:
In 7.5 s at 20 m/s the train travels 20 × 7.5 = 150 m ✅
Quick Variations
1. Two trains passing each other: Distance = sum of lengths. Use relative speed (add or subtract) and ensure units match.
2. Train passing a moving object (e.g., slow train/person): Distance = train length (+ gap if needed). Relative speed = train speed - object speed (same direction) or + (opposite).
3. Lengths in km or mixed units: Convert lengths to consistent units (metres when using seconds, or kilometres when using hours).
4. Platform length sometimes given as 'x times train length': compute numeric platform length first, then sum.
Trick to Always Use
- Step 1: Ask: passing a pole (distance = train length) or platform (distance = train + platform length)?
- Step 2: Convert units so distance and speed are compatible (m with m/s, km with km/h).
- Step 3: If two objects are involved, decide same/opposite direction → relative speed = v1 - v2 or v1 + v2.
- Step 4: Use Time = Distance ÷ Speed; round only at the end and provide seconds/minutes as required.
Summary
Summary
For trains passing poles or platforms:
- Distance to cover = train length (pole) or train + platform length (platform).
- Use consistent units: m and m/s when time in seconds; km and km/h when time in hours.
- Formula: Time = Distance ÷ Speed. For two-train interactions use relative speed and sum of lengths.
- Quick check: multiply computed time by speed to verify the distance equals what you expected.
Hint: For a pole: Time = Train length ÷ (Speed in m/s).
Common Mistakes: Using km/h directly without converting to m/s.