Downstream/Upstream Boat Speed – Important Formulas
Numerical Aptitude Notes for APSC Prelim CSAT Paper, SSC and Competitive Exams
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Still Water: If the speed of the water is zero, i.e. water is stationary, then it is called still water.
Stream: The moving water in the river is known as a stream.
- Upstream: If a boat or a swimmer moves in the opposite direction of the stream, then it is called upstream, i.e. direction against the stream.
- Downstream: If a boar or a swimmer moves in the same direction of the stream, then it is called downstream, i.e. direction along the stream
If the speed of a boat in still water is u km/hr and Speed of the stream is v km/hr,
- Speed downstream = (u + v) km/hr.
- Speed upstream = (u – v) km/hr.
If the speed downstream is a km/hr and the speed upstream is b km/hr, then
- Boat Speed in still water = ½ (Downstream Speed + Upstream Speed) = 1/2 x (a + b) km/hr.
- Rate of stream = ½ (Downstream Speed – Upstream Speed) = 1/2 x (a – b) km/hr.
- Average Speed of Boat = {(Upstream Speed × Downstream Speed) / Boat’s Speed in Still Water}
If it takes “T” hours for a boat to reach a point in still water and comes back to the same point then,
the distance between the two points = {(u2-v2) × T} / 2u,
where “u” is the speed of the boat in still water and “v” is the speed of the stream.
If it takes “T” hours more to go to a point in upstream than downstream for the same distance, then
the distance = {(u2-v2) × t} / 2v,
where “u” is the speed of the boat in still water and “v” is the speed of the stream.
If a boat travels a distance downstream in “t1” hours and returns the same distance upstream in “t2” hours, then,
the speed of the man in still water = [v × {(t2+t1) / (t2-t1)}] km/hr,
where “v” is the speed of the stream