Question

A boat takes $5$ hours to go $300km$ downstream. It takes the same time to go $150km$ upstream. Calculate:
(i) the speed of the boat in still water and
(ii) the speed of the stream

Answer 1

Let the speed of the boast in still water be $xkm/hr$. Let the speed of the stream by $ykm/hr$. Down-stream, the relative speed of the boat is $(x+y)km/hr$ and up-stream its relative speed is $x-ykm/hr$. Using distance $=speed\times time$, we obtain
$300=(x+y)\times 5$, and $150=(x-y)\times 5$.
Thus we have two equations
$x+y=60,..........\left(1\right)$
$x-y=30.........\left(2\right)$
Adding these two, we get $2x=90$ or $x=45$. Hence $y=60-x=60-45=15$.
Therefore the speed of the boat in still water is $45km/hr$. The speed of the steam is $15km/hr$.