The distance between two points is 36 km. A boat rows in still water at 6 kmph. It takes 8 hours less to cover this distance in downstream in comparison to that in upstream. The rate of stream is

Let speed of stream = $$x$$ kmph

=> Speed of boat downstream = $$(6 + x)$$ kmph

Speed upstream = $$(6 - x)$$ kmph

Using, $$time = \frac{distance}{speed}$$

=> $$\frac{36}{6 - x} - \frac{36}{6 + x} = 8$$

=> $$\frac{1}{6 - x} - \frac{1}{6 + x} = \frac{8}{36}$$

=> $$\frac{(6 + x) - (6 - x)}{(6 + x) (6 - x)} = \frac{2}{9}$$

=> $$\frac{2x}{36 - x^2} = \frac{2}{9}$$

=> $$\frac{x}{36 - x^2} = \frac{1}{9}$$

=> $$36 - x^2 = 9x$$

=> $$x^2 + 9x - 36 = 0$$

=> $$x^2 + 12x - 3x - 36 = 0$$

=> $$x (x + 12) - 3 (x + 12) = 0$$

=> $$x = 3 , -12$$

$$\because$$ Speed cant be negative, => $$x = 3$$ kmph