Numerical aptitude · Time and motion
Boats and streams, made easy
💡 The idea
Going with the river (downstream) it helps you: add its speed. Going against it (upstream) it slows you: subtract.
⬇️ Downstream
boat + river→⬆️ Upstream
boat − river
boat + river→⬆️ Upstream
boat − river
🧭 The method: 3 steps
- Downstream speed = boat + river. Upstream = boat − river.
- Use Time = distance ÷ that speed for each part.
- Given down and up speeds? Boat = (down + up) ÷ 2, river = (down − up) ÷ 2.
🎬 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. Boat 10 km/h, river 2 km/h. Time for 36 km downstream?
- Downstream = 10 + 2 = 12 km/h
- Time = 36 ÷ 12 = 3 hours
Example 2. Down 14 km/h, up 8 km/h. River speed?
- Down − up = 14 − 8 = 6 = 2 × river
- River = 6 ÷ 2 = 3 km/h (boat = (14 + 8) ÷ 2 = 11)
⚠️ Where people go wrong
- A round trip does not cancel the river: the slow way costs more time than the fast way saves.
- River = half the difference, not the whole difference.
📌 Remember
- Down = b + s, up = b − s
- b = (down + up) ÷ 2, s = (down − up) ÷ 2