Boats and streams Concept questions come to are special types of time and distance problems. By using different tricks, Concepts, and tactics for boats and streams questions based on still water, downstream, Upstream asked to find the speed of boat or swimmer you can achieve success in competitive exams.
Some Of The Important Terms in Boats and Streams Concept
Still water: speed of water in river=0.
Let the speed of the boat/swimmer in still water is X.
Stream: Speed of water moving in the river (let the speed of stream= Y).
Upstream: boat/swimmer moving against the stream.
Downstream: boat/swimmer moving along with the stream.
when the speed of boat/swimmer is given we usually consider it as speed in still water (i, e Zero).
Boats And Streams Formulas
- The speed of the boat/swimmer in the direction of the stream(downstream) is X+Y.
- The speed of the boat/swimmer in the opposite direction of the stream(upstream) is X-Y.
- speed of the boat/swimmer is
\begin{align*}
\dfrac {\begin{pmatrix} Downstream \\ speed \end{pmatrix}+\begin{pmatrix} Upstream \\ Speed \end{pmatrix}}{2}
\end{align*}
- Speed of the stream is
\begin{align*}
\dfrac {\begin{pmatrix} Downstream \\ speed \end{pmatrix}-\begin{pmatrix} Upstream \\ Speed \end{pmatrix}}{2}
\end{align*}
- A man can row a boat in still water with a speed of x km/h.speed of the stream is y km/h. If he rows d1 distance downstream and d2 distance upstream in t hours, then \begin{align*} \dfrac {d_{1}}{x+y}+\dfrac {d_{2}}{x-y}=t \end{align*}
if he rows same distance d upstream and downstream then
\begin{align*} \dfrac {d}{x+y}+\dfrac {d}{x-y}= \dfrac {t\left( x^{2}-y^{2}\right) }{2x} =t \end{align*}
- A man swims in still water at a speed of x km/h.speed of the stream is y km/h.if he swims same distance upstream and downstream then his average speed during the total journy is \begin{align*}
\dfrac {Upstream\times Downstream}{Man’s \ rate \ in \ still \ water} \\ \\ =\dfrac {\left( x-y\right) \left( x+y\right) }{x} km/h
\end{align*} - A swimmer/boat travels a certain distance downstream and upstream in t1 and t2 hours respectively then, \begin{align*}
\dfrac {speed \ of \ swimmer}{speed \ of \ stream}=\dfrac {t_{1}+t_{2}}{t_{1}-t_{2}}
\end{align*} - A boat/swimmer travels in still water with a speed of x km/h.speed of stream is y km/h. If the boat/swimmer takes n times as long to row upstream as to row downstream the river, then \begin{align*}
x=y\left( \dfrac {n+1}{n-1}\right)
\end{align*}
