The core formula and conversions
Distance = speed × time. Keep units consistent. To convert km/h to m/s, multiply by 5/18; to convert m/s to km/h, multiply by 18/5. For example, 72 km/h = 72 × 5/18 = 20 m/s.
Key results
- Average speed = total distance ÷ total time. For equal distances at speeds a and b, it is 2ab ÷ (a + b).
- Relative speed: moving in opposite directions, add the speeds; in the same direction, subtract them.
- Trains: to cross a pole or a person, the train covers its own length; to cross a platform or another train, it covers the sum of the lengths.
- Boats and streams: downstream speed = boat + stream; upstream = boat − stream.
Worked examples
Example 1. A car travels 60 km at 30 km/h and returns at 60 km/h. Average speed = 2 × 30 × 60 ÷ 90 = 40 km/h.
Example 2. Two trains 300 km apart start towards each other at 60 and 40 km/h. They meet after 300 ÷ 100 = 3 hours.
Example 3 (train and pole). A 150 m train at 54 km/h crosses a pole. 54 km/h = 15 m/s; time = 150 ÷ 15 = 10 seconds.
Example 4 (train and platform). The same train crosses a 250 m platform: distance = 150 + 250 = 400 m; time = 400 ÷ 15 ≈ 26.7 seconds.
Example 5 (boat). A boat goes 24 km downstream in 2 hours and returns upstream in 3 hours. Downstream speed 12, upstream 8 km/h. Boat speed = (12 + 8) ÷ 2 = 10 km/h; stream = (12 − 8) ÷ 2 = 2 km/h.
Example 6 (relative speed, same direction). A runs at 8 m/s and B at 6 m/s, with A 40 m behind B. A catches up after 40 ÷ 2 = 20 seconds.
Common traps
- Averaging two speeds for a round trip.
- Mixing km/h and m/s.
- Forgetting the train's own length when crossing a platform.
- Using the wrong direction for relative speed.
Speed tips
- Memorise 5/18 and 18/5 and a few conversions: 36 km/h = 10 m/s, 54 = 15, 72 = 20, 90 = 25.
- If speeds are in ratio a : b over the same distance, times are in ratio b : a.
- For meeting problems, use total distance ÷ combined speed.
A practice routine
- Day 1: formula and unit conversions, ten questions.
- Day 2: average speed and ratios of speed and time.
- Day 3: relative speed and trains.
- Day 4: boats and streams; a timed set of 12 questions at 60 seconds each.
Where it appears
This topic appears in SSC CGL, banking, railway mathematics, CAT and MAT papers. It pairs with time and work and ratio and proportion.
Practice tests below are published by institutes and educators on TestMint.
