Problems on Trains: Formulas, Methods and Examples
Problems on Trains use distance, speed and time to calculate how long a train takes to cross a pole, person, platform or another train. The distance covered equals the train length, the sum of train and platform lengths, or the sum of train lengths. Relative speed determines the time when two objects are moving.
What Are Problems on Trains?
For a train crossing a pole or person, the distance is the train's length. For crossing a platform, the distance is train length + platform length. For crossing another train, the distance is the sum of both train lengths. Use relative speed for two moving trains: add speeds in opposite directions and subtract speeds in the same direction.
Problems on Trains Formula & Tricks
Important Formulas
Use consistent units for distance and speed. If distance is in metres and speed is in metres per second, time is in seconds.
Convert km/h to m/s before using train lengths given in metres.
A stationary pole or person has negligible length, so the distance covered is equal to the train length.
The train crosses the platform only when its rear end leaves the far end of the platform.
Speeds are added because the distance between the trains decreases at the sum of their speeds.
Use the difference of speeds as the relative speed. The faster train must cover the combined lengths to completely overtake the slower train.
Quick Tricks
When length is in metres and speed is in km/h, multiply the speed by 5/18 first. This avoids incorrect time units.
For a platform or another train, add the relevant lengths. Crossing means the entire rear of the train has passed the object or the other train.
Add speeds for opposite directions and subtract speeds for the same direction. Then divide the required distance by this relative speed.
Problems on Trains Concepts
A Train Crossing a Pole or Person
Apply time = distance ÷ speed. Convert the train speed to m/s when the length is in metres. The pole or person is treated as having zero length.
A Train Crossing a Platform
The front of the train first reaches the platform and the rear must completely leave it. Therefore, distance = train length + platform length, and time = total distance ÷ train speed.
Two Trains Crossing in Opposite Directions
Use time = (Length₁ + Length₂) ÷ (Speed₁ + Speed₂). Both trains move towards each other, so the gap closes faster than the speed of either train alone.
Two Trains Moving in the Same Direction
Use time = (Length₁ + Length₂) ÷ (Faster speed − Slower speed). Complete overtaking occurs only after the faster train's rear has passed the slower train's front.
Problems on Trains Video Lessons
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Trains Crossing a Pole or Person
Learn how to calculate the time, speed, or length of a train when it crosses a pole or a person using the appropriate distance and speed relationships.
Practice Problems on Trains Questions
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Problems on Trains: Quick Revision
Use the direction of motion and the required crossing condition to select the distance and relative-speed formula.
- For a pole or person, distance = train length.
- For a platform, distance = train length + platform length.
- For two trains, distance = sum of their lengths for complete crossing or overtaking.
- Opposite-direction relative speed = sum of speeds.
- Same-direction relative speed = difference of speeds.
- Convert km/h to m/s by multiplying by 5/18.
- Time = distance ÷ speed, with distance and speed in compatible units.
Problems on Trains FAQs
What formula is used when a train crosses a pole?
Time = Train length ÷ Train speed. If length is in metres, express speed in m/s.
How is the time to cross a platform calculated?
Time = (Train length + Platform length) ÷ Train speed. For example, a 200 m train crossing a 300 m platform at 25 m/s takes 500 ÷ 25 = 20 seconds.
Why are speeds added when two trains move in opposite directions?
Their distance decreases at the sum of their speeds. Thus, relative speed = Speed₁ + Speed₂.
Why are speeds subtracted when two trains move in the same direction?
The faster train gains on the slower train at the difference of their speeds. Thus, relative speed = Faster speed − Slower speed.
A train is 240 m long and moves at 60 km/h. How long does it take to cross a pole?
60 km/h = 60 × 5/18 = 50/3 m/s. Time = 240 ÷ (50/3) = 14.4 seconds.
What distance is used when one train completely overtakes another?
Use the sum of the two train lengths. The faster train must cover this combined length relative to the slower train.