In this guide
Every question in this topic comes back to one line: distance = speed × time. What changes is the setting. A bus runs between towns, a person goes and comes back at different speeds, two trains pass each other. In a railway exam you can expect trains, so train problems get special attention below.
Two habits prevent most errors: put every quantity in the same units before you calculate, and when a train crosses something, add the lengths correctly.
The basic formula
- Distance = Speed × Time
- Speed = Distance ÷ Time
- Time = Distance ÷ Speed
If the time is fixed, distance and speed go up together. If the distance is fixed, a higher speed means less time: speed and time are in inverse ratio. At speeds in the ratio 3 : 4, the times for the same distance are in the ratio 4 : 3.
Changing units
| Change | Multiply by | Example |
|---|---|---|
| km/h → m/s | 5/18 | 72 km/h = 20 m/s |
| m/s → km/h | 18/5 | 15 m/s = 54 km/h |
| minutes → hours | ÷ 60 | 45 minutes = 3/4 hour |
Why 5/18? 1 km/h = 1,000 m in 3,600 s = 5/18 m/s. Learn a few pairs: 18 km/h = 5 m/s, 36 = 10, 54 = 15, 72 = 20, 90 = 25.
Average speed
Average speed = total distance ÷ total time. It is not the simple average of the speeds.
For a round trip, or any two equal distances, at speeds a and b:
- Average speed = 2ab ÷ (a + b)
Relative speed
When two things move at once, treat one as standing still and give the other the relative speed:
- Moving towards each other (opposite directions): add the speeds.
- Moving in the same direction: subtract the speeds.
Trains
A train has length, so crossing something means the whole train must pass. The distance covered is the train's own length plus the length of whatever it crosses.
| Train crosses | Distance to cover | Speed to use |
|---|---|---|
| A pole, signal or standing person | Train length | Train speed |
| A platform, bridge or tunnel | Train length + platform length | Train speed |
| A train coming the other way | Sum of both lengths | Sum of speeds |
| A train going the same way | Sum of both lengths | Difference of speeds |
Boats and streams
A boat going with the current (downstream) is helped; against it (upstream) it is slowed. With b = speed of the boat in still water and s = speed of the stream:
- Downstream speed = b + s
- Upstream speed = b − s
Worked examples
Example 1: A person goes to a town at 30 km/h and returns at 60 km/h. Find the average speed.
- Equal distances, so use 2ab ÷ (a + b).
- 2 × 30 × 60 ÷ 90 = 3,600 ÷ 90 = 40 km/h. Not 45.
Example 2: A 120 m train runs at 36 km/h. How long does it take to cross a pole, and then a 180 m bridge?
- 36 km/h = 10 m/s.
- Pole: 120 ÷ 10 = 12 seconds.
- Bridge: (120 + 180) ÷ 10 = 30 seconds.
Example 3: Two trains, 150 m and 100 m long, run on parallel tracks at 60 km/h and 30 km/h. How long do they take to cross each other if they move in opposite directions?
- Relative speed = 90 km/h = 25 m/s. Distance = 250 m.
- Time = 250 ÷ 25 = 10 seconds.
Example 4: The same two trains now move in the same direction. How long does the faster one take to pass the slower one?
- Relative speed = 30 km/h = 30 × 5/18 = 25/3 m/s.
- Time = 250 ÷ 25/3 = 250 × 3 ÷ 25 = 30 seconds.
Example 5: Walking at 5 km/h, a person reaches the station 6 minutes late. Walking at 6 km/h, they reach 4 minutes early. How far is the station?
- The two times differ by 6 + 4 = 10 minutes = 1/6 hour.
- d/5 − d/6 = 1/6, so d/30 = 1/6, and d = 5 km.
- Check: 5 km takes 60 minutes at 5 km/h and 50 minutes at 6 km/h. The gap is 10 minutes.
Common mistakes
- Mixing km/h and m/s in one calculation.
- Taking the simple average of two speeds for a round trip.
- Forgetting the platform or bridge length, or the second train's length.
- Adding speeds for trains moving the same way.
- Leaving minutes as minutes when the speed is in km/h.
Practice set
- Convert 90 km/h to m/s.
- Convert 20 m/s to km/h.
- A 150 m train at 54 km/h crosses a 300 m platform. How long does it take?
- Two trains, each 100 m long, run towards each other at 40 km/h and 50 km/h. How long do they take to cross each other?
- A train crosses a pole in 15 seconds and a 150 m platform in 25 seconds. Find its length and speed.
- A car covers 60 km at 30 km/h and the next 60 km at 60 km/h. Find its average speed.
- A person covers a distance in 3 hours at 40 km/h. At what speed must they travel to cover it in 2 hours 30 minutes?
- A boat's speed in still water is 10 km/h and the stream flows at 2 km/h. How long does it take to go 24 km downstream?
Answers:
- 25 m/s. 90 × 5/18.
- 72 km/h. 20 × 18/5.
- 30 seconds. 54 km/h = 15 m/s; (150 + 300) ÷ 15.
- 8 seconds. Relative speed 90 km/h = 25 m/s; 200 ÷ 25.
- 225 m and 54 km/h. The extra 150 m takes 10 extra seconds, so speed = 15 m/s; length = 15 × 15 = 225 m.
- 40 km/h. Total 120 km in 2 + 1 = 3 hours.
- 48 km/h. Distance 120 km; 120 ÷ 2.5.
- 2 hours. Downstream speed 12 km/h; 24 ÷ 12.
What to do next
- Learn the km/h–m/s pairs (18, 36, 54, 72, 90) until you convert without writing.
- Solve ten train questions, filling in "distance" and "speed" from the table before calculating.
- Practise three average-speed questions and check that your answer is not the simple average.
- Revise time and work, which uses the same rate × time idea, and ratio for speed–time ratios.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Railway Recruitment Boards website .
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