Boats and Streams: Concepts and Theory

The topic of Boats and Streams is very important as there are questions in almost every competitive examination from this area. The concept is easy to understand and is related to the topic of Time, Speed and Distance. Let us start the topic with basic definitions.
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  • A boat is said to go downstream if it is moving along the direction of the stream. The net speed of the boat in this case is called downstream speed.
  • A boat is said to go upstream if it is moving in the direction opposite to the direction of the stream. The net speed of the boat in this case is called upstream speed.
Let the speed of the boat in still water is 'b' km/hr and the speed of the stream is 'w' km/hr. When the boat goes downstream then the speed will be (b + w) km/hr as in this case the water will take the boat along with it.
When the boat goes upstream then the speed will be (b - w) km/hr as in this case the water will offer resistance to the boat.
Let the downstream speed = d = b + w ……….(i)
Then the upstream speed = u = b – w ………(ii)
Adding the two equations, we get 2b = d + u.
⇒ b = (d+u) / 2 which gives the speed of the boat in terms of downstream and upstream speed. Subtracting the equation (i) and (ii), we get d – u = 2w ⇒ w = (d-u) / 2 which gives the speed of the stream in terms of downstream and upstream speed. You should remember these boats and streams formulas.
Some Important Shortcuts:
  • Suppose a man can row a boat at a speed of r km/hr in still water and covers the same distance up and down in a stream while a stream flows at a speed of s km/hr. His average speed will be :
  • A man rows downstream by covering a certain distance in p1 hours and returns the same distance upstream in p2 hours. If the speed of the stream is s km/hr, then the speed of the man in still water will be :
  • A man takes same number of times say m times to row upstream as to row downstream a river. If the speed of the man is r km/hr and the speed of the stream is s km/hr, then
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