Time, Speed & Distance
One relationship drives this entire topic: distance = speed × time. Everything else — trains, boats, relative motion — is that formula with a sign convention. The marks are lost on unit conversion and on deciding whether speeds add or subtract.
Updated 19 September 2026 · Trains and relative speed appear in most campus papers.
How to think about time, speed & distance
Convert units before anything else
Mixing km/h with metres and seconds is the most common source of wrong answers here. Convert first, solve second. km/h to m/s is × 5/18; m/s to km/h is × 18/5. Trains are almost always metres and seconds.
Relative speed: add when opposite, subtract when same
Two objects moving towards each other close the gap at the sum of their speeds. Moving in the same direction, the faster gains on the slower at the difference. Decide the direction first, then pick the operation.
What a train has to cross
To pass a pole, a train covers its own length. To pass a platform or another train, it covers its own length plus the length of the thing it is passing. Missing the second length is a standard trap.
Average speed is not the average of speeds
For equal distances at speeds x and y, the average speed is the harmonic mean 2xy/(x+y), not (x+y)/2. You spend more time at the slower speed, so it pulls the average down more than the fast leg pulls it up.
Formulas and shortcuts
- Core relation
Distance = Speed × Time - km/h to m/s
multiply by 5/18 - m/s to km/h
multiply by 18/5 - Relative speed, opposite directions
a + b - Relative speed, same direction
|a − b| - Train crossing a pole
Time = Length of train / Speed - Train crossing a platform
Time = (Length of train + Length of platform) / Speed - Average speed, equal distances
2xy / (x + y)Harmonic mean, not arithmetic mean.
- Downstream speed
Boat speed + Stream speed - Upstream speed
Boat speed − Stream speed
Solved examples
Q1. A train 200 m long runs at 72 km/h. How long does it take to pass a pole?
- Convert speed to m/s first, because the length is in metres.
- 72 km/h = 72 × 5/18 = 20 m/s
- To pass a pole the train covers just its own length, 200 m.
- Time = 200 / 20
Answer: 10 seconds
Q2. A train 150 m long travelling at 54 km/h crosses a platform 150 m long. How long does it take?
- 54 km/h = 54 × 5/18 = 15 m/s
- Distance covered = train length + platform length = 150 + 150 = 300 m
- Time = 300 / 15
Answer: 20 seconds
Against a pole it would have been 150/15 = 10 s — the platform doubles it here.
Q3. A man travels from A to B at 40 km/h and returns at 60 km/h. What is his average speed for the whole journey?
- The distances are equal, so use the harmonic mean, not (40+60)/2.
- Average = 2xy / (x + y) = (2 × 40 × 60) / (40 + 60)
- = 4800 / 100
Answer: 48 km/h
Verify with a real distance: 120 km each way. Out = 3 h, back = 2 h. Total 240 km in 5 h = 48 km/h. Not 50.
Practice questions with answers
1. A car covers 180 km in 3 hours. Its speed is:
Answer: B. 60 km/h — 180 / 3 = 60 km/h.
2. 90 km/h expressed in m/s is:
Answer: B. 25 m/s — 90 × 5/18 = 25 m/s.
3. Two trains move towards each other at 60 km/h and 40 km/h. Their relative speed is:
Answer: C. 100 km/h — Opposite directions, so speeds add: 60 + 40 = 100 km/h.
4. A boat travels at 10 km/h in still water; the stream flows at 2 km/h. Downstream speed is:
Answer: C. 12 km/h — Downstream = 10 + 2 = 12 km/h (upstream would be 8 km/h).
5. A train 120 m long at 36 km/h crosses a pole in:
Answer: B. 12 s — 36 km/h = 10 m/s. Time = 120 / 10 = 12 s.
6. A man goes uphill at 30 km/h and returns downhill at 60 km/h. Average speed is:
Answer: A. 40 km/h — (2 × 30 × 60) / 90 = 3600 / 90 = 40 km/h.
7. Walking at 5 km/h a man reaches office in 30 minutes. Walking at 6 km/h he takes:
Answer: B. 25 min — Distance = 5 × 0.5 = 2.5 km. Time at 6 km/h = 2.5 / 6 h = 0.4167 h = 25 minutes.
8. Two trains 100 m and 150 m long run in opposite directions at 40 km/h and 50 km/h. Time to cross each other:
Answer: B. 10 s — Opposite directions, so speeds add: 40 + 50 = 90 km/h = 90 × 5/18 = 25 m/s. Each train must clear the other entirely, so the distance is 100 + 150 = 250 m. Time = 250 / 25 = 10 s.
Where marks get lost
- Solving in km/h while the lengths are in metres.
- Forgetting to add the platform or second train length.
- Taking the arithmetic mean of two speeds instead of the harmonic mean.
- Adding speeds when the objects move in the same direction.
Reading is not practising.
Run a timed set on time, speed & distance and see which step you actually lose time on. Free, no card needed.
Start a timed set