The current of a stream runs at 2 kmph. A boat goes 16 km and back to the starting point in 6 hours. The speed of the boat in still water is?

Solution: The  speed of  a stream = 2 kmph

In down stream = (x + 2) kmph

In up stream = (x – 2) kmph

$\therefore \frac{16}{(x+2)}+\frac{16}{(x-2)}=6$

$16\left[\frac{x+2+x-2}{x^2-4}\right]=6$

$\frac{2x}{x^2-4}=\frac{6}{16}$

$\frac{2x}{x^2-4}=\frac{3}{8}$

$16x=3x^2-12=0$

$3x^2-16x-12=0$

$3x^2-18x+2x-12=0$

$3x(x-6)+2(x-6)=0$

$\underset{\_}{(x-6)}(3x+2)=0$

$x=6$