Question

A sailor can row a boat $8$ km downstream and return back to the starting point in $1$ hr. $40$ min. If the speed of the stream is $2$ km/hr, find the speed of boat in still water.

Answer 1

Speed of the stream $=2$ km/hr

Let speed of the boat in still water be $x$ km/hr.

Time taken to travel downstream $=\frac{8}{x+2}$

Time taken to travel upstream $=\frac{8}{x-2}$

Total time $=1$ hr. $40$ min $=\frac{5}{3}$ hr.

Therefore, $\frac{8}{x+2}+\frac{8}{x-2}=\frac{5}{3}$

$\Rightarrow 3(8x-16+8x+16)=5(x^2-4)$

$\Rightarrow 24x+24x=5x^2-20$

$\Rightarrow 5x^2-48x-20=0$

$\Rightarrow 5x^2-50x+2x-20=0$

$\Rightarrow 5x(x-10)+2(x-10)=0$

$\Rightarrow (x-10)(5x-2)=0$

$\Rightarrow x=10,\frac{2}{5}$

As speed cannot be in fraction, $x=10$ is the correct value.

Thus, speed of boat in still water is $10$ km/hr.