A man can row 24 km upstream and 54 km downstream in 6 hours. He can also row 36 km upstream and 48 km downstream in 8 hours. What is the speed of the man in still water ?

Let speed of man upstream = $$x$$ km/h

and speed of man downstream = $$y$$ km/h

Acc to ques,

=> $$\frac{24}{x} + \frac{54}{y} = 6$$

=> $$\frac{4}{x} + \frac{9}{y} = 1$$ -------------Eqn(1)

and $$\frac{36}{x} + \frac{48}{y} = 8$$

=> $$\frac{9}{x} + \frac{12}{y} = 2$$ -------------Eqn(2)

Solving equations (1) & (2), we get :

=> $$x = \frac{11}{2}$$ and $$y = 33$$

$$\therefore$$ Speed of man in still water = $$\frac{1}{2}$$ (downstream + upstream)

= $$\frac{1}{2} (\frac{11}{2} + 33)$$

= $$\frac{77}{4} = 19.25$$ km/h