Boats and Streams Cheat Sheet
31 Oct 2026
Quick answer
A quick revision cheat sheet on boats and streams for SSC, Banking, Railway and state exams. It covers downstream and upstream speed, how to recover the boat's speed in still water and the stream's speed, the average-speed idea, and the time taken for a round trip, with worked examples to revise quickly.
Boats and Streams Cheat Sheet
Quick Revision
In boats and streams problems a boat moves through water that is itself flowing. Let b be the boat's speed in still water and s the speed of the stream.
1. Downstream and Upstream Speed
Downstream speed = b + s (moving with the current)
Upstream speed = b − s (moving against the current)Downstream is always the faster direction.
2. Recovering the Two Speeds
If you know the downstream speed D and the upstream speed U:
b = (D + U) / 2 (boat in still water)
s = (D − U) / 2 (stream)3. Time for a Journey
Time = Distance / SpeedUse the downstream speed for the with-current leg and the upstream speed for the against-current leg.
4. Worked Example
A boat does 10 km/h in still water; the stream flows at 2 km/h.
Downstream = 10 + 2 = 12 km/h
Upstream = 10 − 2 = 8 km/hGiven instead D = 12 and U = 8: b = (12 + 8)/2 = 10, s = (12 − 8)/2 = 2.
5. Exam Quick Tips
- The boat's speed is the average of the downstream and upstream speeds; the stream's is half their difference.
- Going down then up over the same distance takes longer than twice the still-water time.
- Keep all speeds in the same unit before dividing for time.
Keep revising with the rest of the Maths section:
How this was made: Drafted with AI assistance; spot-checked by the editor on 31 October 2026.