Important Formulas - Boats and Streams - Tricks & Shortcuts

1. Downstream/Upstream:

In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream.

2. If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then:

Speed downstream = (u + v) km/hr.

Speed upstream = (u - v) km/hr.

3. If the speed downstream is a km/hr and the speed upstream is b km/hr, then:

Speed in still water = (1/2)(a + b) km/hr.

Rate of stream = (1/2)(a - b) km/hr.

4. Assume that a man can row at the speed of x km/hr in still water and he rows the same distance up and down in a stream which flows at a rate of y km/hr.

Then his average speed throughout the journey
                                       = (Speed downstream × Speed upstream)/ Speed in still water
                                       = ((x+y) (x-y))/x    km/hr

5. Let the speed of a man in still water be x km/hr and the speed of a stream be y km/hr. If he takes t hours more in upstream than to go downstream for the same distance, the distance

                      = ((x²-y²)t)/2y     km

6. A man rows a certain distance downstream in t₁ hours and returns the same distance upstream in t₂hours. If the speed of the stream is y km/hr, then the speed of the man in still water

                        = y ((t₂+ t₁)/ (t₂- t₁)) km/hr

7. A man can row a boat in still water at x km/hr. In a stream flowing at y km/hr, if it takes him t hours to row a place and come back, then the distance between the two places

                   = (t (x²-y²))/2x   km

8. A man takes n times as long to row upstream as to row downstream the river. If the speed of the man is x km/hr and the speed of the stream is y km/hr, then

                       x  =   y ((n+ 1)/ (n-1))
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