A man takes 2.2 times as long to row a distance upstream as to row the same distance downstream. If he can row 55 km downstream in 2 hours 30 minutes, what is the speed of the boat in still water? (in km/h)

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

=> Speed of current = $$y$$ km/hr

Let distance travelled = $$d$$ km

Acc. to ques, => $$2.2 (\frac{d}{x + y}) = \frac{d}{x - y}$$

=> $$2.2x - 2.2y = x + y$$

=> $$2.2x - x = y + 2.2y$$

=> $$3x = 8y$$ -------------(i)

Also, the man takes 2 hrs 30 mins in travelling 55 km downstream.

=> $$\frac{55}{x + y} = 2 + \frac{1}{2}$$

=> $$\frac{55}{x + y} = \frac{5}{2}$$

=> $$x + y = 22$$

Multiplying both sides by 8, and using eqn(i), we get :

=> $$8x + 3x = 22 \times 8$$

=> $$x = \frac{22 \times 8}{11} = 16$$ km/hr