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Quantitative Aptitude›Ch 3: Time, Work & Distance›Boats and Streams
Master upstream and downstream speed concepts for competitive exams
When a boat moves in the same direction as the stream, it is called downstream motion and speeds are added. When it moves against the stream, it is upstream motion and speeds are subtracted. Always denote boat speed as u and stream speed as v.
Quick Memory Hooks
| Parameter | Notation | Formula |
|---|---|---|
| Downstream Speed | D | u + v |
| Upstream Speed | U | u - v |
| Speed of Boat (u) | u | (D + U) / 2 |
| Speed of Stream (v) | v | (D - U) / 2 |
Downstream
(With the flow)
With the flow
Boat and river currents push together, increasing total speed.
Upstream
(Against the flow)
Against the flow
Boat fights the current, reducing effective speed.
Still Water
(No river flow)
No river flow
Speed of the boat alone without any stream interference.
Stream Speed
(Water velocity)
Water velocity
The speed at which the river itself moves forward.
Adding speeds in upstream motionAlways subtract v from u for upstream
Students often add speeds out of habit. Upstream always means resistance, hence subtraction.
Confusing km/hr with m/secMultiply by 5/18 to convert km/h to m/s
Always check unit consistency between distance given in meters and speed in km/hr.
Assuming still water speed is D + UStill water speed is (D + U) / 2
Still water speed is the arithmetic mean of downstream and upstream speeds, not their sum.
Q1.A boat goes 15 km/hr downstream and 9 km/hr upstream. What is the speed of the boat in still water?
Q2.A man rows upstream 11 km and downstream 26 km, taking 5 hours for each journey. What is the speed of the stream?