Quick Review: Boats and Streams

Important Terms

• 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.
• Downstream: If a boar or a swimmer moves in the same direction of the stream, then it is called downstream.
• When the speed of a boat or a swimmer is given, it usually means speed in still water.

Formulae

• Upstream Speed: It is the speed of the boat against the stream = (u - v) km/hr
• Downstream Speed: It is the speed of the boat with the stream = (u + v) km/hr
• If upstream is denoted as U_S and downstream as D_S, then:
  Speed of boat or swimmer in still water = 1/2 (D_s + U_s)
  Speed of stream =1/2 (D_s - U_s)
• If a man is capable of rowing at the speed of u km/hr in still water, rows the equal distance up and down the stream which flows at a rate of v km/hr, then the average speed throughout the journey
• A man can row a boat in still water at u km/hr. A stream is flowing at v km/hr and it take t hrs more in upstream than to go downstream for the same distance, then the distance is calculated by = (u² – v²)t/2v km
• A man rows a certain distance downstream in t₁ hrs and returns the same distance upstream in t₂ hrs. If the speed of the stream is v km/hr, then the speed of the man in still water will be calculated by
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• A man can row a boat in still water at u km/hr. In a stream flowing at v km/hr if it takes him t hrs to row to a place and come back, then the distance between the two places is
• A boat or a swimmer takes n times as long as to row upstream as to row downstream the river. If the speed of the boat or the swimmer is u km/hr in still water and speed of stream is v km/hr, then