Problems on Trains
A train crossing something covers its own length plus that thing's length. A pole or a man counts as length zero.
Why this topic matters
A train is not a dot. To pass a pole it must move its whole length. To cross a platform it must move its length plus the platform's.
Train questions are time and distance with one twist: the train's own length is part of the distance.
Pole or person vs platform or bridge
Passing a pole, a signal post or a standing person: distance = length of the train.
Crossing a platform, bridge or tunnel: distance = length of the train + length of the platform.
- Speed = 240 / 12 = 20 m/s.Passing a pole: distance = train length.
- Platform: distance = 240 + 360 = 600 m.
- 600 / 20 = 30 seconds.
Two trains
Two trains passing each other cover the SUM of their lengths. Opposite directions: relative speed = sum of speeds. Same direction: difference.
- Relative speed = 54 + 36 = 90 km/h = 25 m/s.Opposite directions add; convert to m/s.
- Distance = 150 + 100 = 250 m.Both lengths.
- 250 / 25 = 10 seconds.
- Relative speed = 72 - 6 = 66 km/h = 55/3 m/s.Same direction subtracts.
- 200 / (55/3) = 600/55 = 120/11 seconds, about 10.9 s.
Formula summary
Shortcuts and tricks
Pole and platform together
Use it when: 'Crosses a pole in 15 s and a 100 m platform in 25 s'.
- The extra 10 s is the platform: speed = 100/10 = 10 m/s.
- Length = 10 × 15 = 150 m.
- 150 m.
Before you move on, you should be able to...
- add the platform length when crossing it
- add both lengths when two trains pass
- use relative speed for trains and walkers
Practice questions (9)
Try each one before opening the solution. Or practise them one by one so your score is saved.
easy A 150 m train at 54 km/h passes a pole in?
- 54 km/h = 15 m/s.
Answer: 10 s
easy A 150 m train at 72 km/h crosses a 250 m platform in?
- 400/20.
Answer: 20 s
easy How long does a train 150 m long, running at 54 km/h, take to pass a telegraph post?
- 54 km/h = 15 m/s.x 5/18.
- Distance = 150 m.A post: only the train's length.
- 150 / 15 = 10 seconds.
Answer: 10 s
medium Trains 120 m and 180 m long run towards each other at 50 and 40 km/h. Time to cross?
- 90 km/h = 25 m/s. 300/25.
Answer: 12 s
medium Trains 100 m and 80 m, same direction, 60 and 42 km/h. Time for the faster to pass the slower?
- 18 km/h = 5 m/s. 180/5.
Answer: 36 s
hard Two trains leave A and B towards each other at the same time. After meeting, they take 9 h and 16 h to reach B and A. Ratio of speeds?
- √(16) : √(9).
Answer: 4:3
hard A train at 54 km/h passes a man walking at 6 km/h in the same direction in 12 s. Length of the train?
- Relative 48 km/h = 40/3 m/s.
- 40/3 × 12 = 160 m.
Answer: 160 m
hard A train passes two men walking the same way at 2 km/h and 4 km/h in 9 s and 10 s. Train speed?
- (v - 2) × 9 = (v - 4) × 10 (same length).
- v = 22.
Answer: 22 km/h
hard Trains of 150 m and 200 m cross each other in 10 s going opposite ways and in 50 s going the same way. Faster train's speed in m/s?
- Sum of speeds 350/10 = 35, difference 350/50 = 7.
- Faster = (35 + 7)/2.
Answer: 21 m/s
Class plan (2 hours, for trainers)
A tested order for teaching this topic in one 2-hour session. Present mode follows the same order.
| 10 min | Warm-up: km/h to m/s. |
| 30 min | Pole vs platform with the diagrams. |
| 30 min | Two trains, both directions; a man walking. |
| 40 min | Practice set. |
| 10 min | Recap. |