Numerical aptitude · Time and motion
Speed, time and distance, made easy
💡 The idea
Distance = speed × time. Everything else comes from moving those three around.
DS × T
🧭 The method: 3 steps
- Write down what you know: distance, speed, time. Check the units match (km with h, m with s).
- Use D = S × T (or S = D ÷ T, T = D ÷ S).
- For two things moving: towards each other add speeds, same way subtract.
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
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✏️ Worked examples
Example 1. What is 72 km/h in m/s?
- 1 km/h = 1000 m ÷ 3600 s = 5/18 m/s
- 72 × 5/18 = 20 m/s
⚡ Shortcut: × 5/18 for km/h → m/s; × 18/5 the other way.
Example 2. Out at 40 km/h, back at 60 km/h. Average speed?
- Take a distance that fits both: 120 km
- Out: 120 ÷ 40 = 3 h. Back: 120 ÷ 60 = 2 h
- Average = 240 km ÷ 5 h = 48 km/h (not 50!)
⚡ Shortcut: 2 × 40 × 60 ÷ (40 + 60) = 48.
Example 3. Two cars 300 km apart drive towards each other at 40 and 60 km/h. When do they meet?
- The gap closes at 40 + 60 = 100 km/h
- Time = 300 ÷ 100 = 3 hours
⚠️ Where people go wrong
- Average speed for the same distance both ways is not the middle of the two speeds.
- Mix km/h with metres and seconds and the answer is off: convert first.
- Towards each other: add. Same direction: subtract.
📌 Remember
- D = S × T
- km/h → m/s: × 5/18
- Round trip average = 2uv ÷ (u + v)