A boat takes six hours to travel a certain distance downstream and five hours to travel a certain distance upstream. The distance travelled upstream is half of the travelled downstream. If the speed of the current is 4 km/hr, what is the speed of the boat in still water? (in km/hr)

Let speed of boat in still water = $$x$$ km/hr

Let distance travelled downstream = $$2d$$ km

=> Distance travelled upstream = $$d$$ km

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

=> $$6 = \frac{2d}{x + 4}$$ ---------(i)

and $$5 = \frac{d}{x - 4}$$ ---------(ii)

Dividing eqn(i) from (ii), we get :

=> $$\frac{6}{5} = \frac{\frac{2d}{x + 4}}{\frac{d}{x - 4}}$$

=> $$\frac{6}{5} = \frac{2 (x - 4)}{x + 4}$$

=> $$6x + 24 = 10x - 40$$

=> $$10x - 6x = 24 + 40 = 64$$

=> $$x = \frac{64}{4} = 16$$ km/hr