Boat and Stream Formulas

• If speed of stream is ‘a’ and a boat (swimmer) takes ‘n’ times as long to row up as to row down the river, then

Speed of Boat (swimmer) in still water = a*(n+1)/(n-1)

• A person can row at a speed of ‘x’ in still water. If stream is flowing at a speed of y, it takes time ‘T’ to row to a place and back, then

Distance between two places = T*(x² – y²) / 2x

• A man rows a certain distance downstream in ‘x’ hour and returns the same distance in ‘y’ hour. When the stream flows at the rate of ‘a’ km/h, then

Speed of the man in still water = a*(x+ y) / (y – x)

• If boat’s speed in still water is ‘a’ km/h and river is flowing with a speed of ‘b’ km/h, then average speed in going to a certain place and coming back to starting point is given by

(a + b)(a – b) / a km/h

• When boat’s speed in still water is ‘a’ km/h and river is flowing with a speed of ‘b’ km/h and time taken to cover a certain distance upstream is ‘T’ more that the time taken to cover the same distance downstream, then

Distance = (a² – b²)*T / 2b

• If a man covers ‘I’ km distance in ‘t₁’ hour along the direction of the river and he covers same distance in ‘t₂' hour against the direction of the river, then

Speed of man = 1/2 * (I/t₁ + I/t₂)

Speed of stream = 1/2 * (I/t₁ – I/t₂)