Train problems involve calculating time taken by trains to cross objects like poles, platforms, bridges, or other trains. The key is understanding that trains have length, unlike point objects
💡Key Rules
When a train crosses a stationary object like a pole, it travels a distance equal to its own length. When crossing a platform or bridge, it travels its own length plus the length of the platform/bridge. For two trains, use relative speed concept
🔑Essential Formulas
Time = Distance/Speed
Speed = Distance/Time
Relative Speed (same direction) = |S1 - S2|
Relative Speed (opposite direction) = S1 + S2
Speed conversion: km/hr to m/s multiply by 5/18, m/s to km/hr multiply by 18/5
📊
Exam Patterns
What examiners ask — read before attempting PYQs
💡Remember
72 km/hr = 20 m/s (this conversion appears frequently)
✏️Worked Example 1
1
Distance covered = Length of train = 120m
2
Time taken = 8 seconds
3
Speed = Distance/Time = 120/8 = 15 m/s
4
Convert to km/hr = 15 × 18/5 = 54 km/hr
Answer: 54 km/hr
Worked Example 2: Two trains of lengths 100m and 150m are running in opposite directions at speeds 40 km/hr and 50 km/hr respectively. In how much time will they cross each other?
Relative speed = 100/9 + 125/9 = 225/9 = 25 m/s (opposite direction, so add)
3
Total distance = 100 + 150 = 250m
4
Time = Distance/Speed = 250/25 = 10 seconds
Answer: 10 seconds
Advanced Shortcut - Platform Formula: Time to cross platform = (Train length + Platform length)/Speed. This direct formula saves calculation steps in exams
→Most Common Trap
Students forget to add platform/bridge length when train crosses them. They only consider train length, leading to wrong answers. Always read whether the train crosses a pole (only train length) or platform/bridge (train length + platform/bridge length).
Another frequent mistake is wrong unit conversion. Practice the 5/18 conversion thoroughly.
Many students confuse when to multiply or divide
⚡Speed-Distance-Time Shortcut
If train crosses pole in time T1 and platform in time T2, then platform length = speed × (T2 - T1). This eliminates the need to calculate train length first.
A train travels 240 km in 4 hours at a constant speed. How long will it take to cover 360 km at the same speed?
Practice 2medium
Train A and Train B are moving towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are initially 300 km apart, in how many hours will they meet?
Practice 3hard
Two trains, A and B, start simultaneously from stations X and Y respectively, which are 480 km apart. Train A travels towards Y at 60 km/h, while train B travels towards X at 40 km/h. After they meet, train A takes 4 more hours to reach Y, while train B takes 9 more hours to reach X. However, train A suddenly reduces its speed by 20% after meeting train B. At what time (in hours from the start) do the two trains actually meet?
60-Second Revision — Trains
Remember: Pole crossing uses only train length, platform crossing adds platform length
Formula: Speed conversion km/hr to m/s multiply by 5/18
Trap: Always check if crossing pole or platform - different distance calculations
Shortcut: 72 km/hr = 20 m/s conversion for quick calculations
Relative speed: Add for opposite direction, subtract for same direction
Two trains: Total distance = Length1 + Length2, use relative speed
Platform trick: Time difference method gives platform length directly