A motorboat travels 28 km downstream and immediately returns and takes double time in returning. If river flow is twice, then boat takes 672 min in going downstream and upstream. Find speed of boat in still water and speed of river flow?

9 km/hr, 3 km/hr

Let boat speed = x, stream speed = y

Condition (i)

⇒ \(\frac{\frac{28}{x\;+\;y}}{\frac{28}{x\;-\;y}}\) = \(\frac{1}{2}\)

⇒ \(\frac{x\;-\;y}{x\;+\;y}\) = \(\frac{1}{2}\)

⇒ x  :  y = 3  :  1 = 3R : 1R

Condition (ii) → 

⇒ \(\frac{28}{x\;+\;2y}\) + \(\frac{28}{x\;-\;2y}\) = \(\frac{672}{60}\)

⇒ \(\frac{28}{3R\;+\;2R}\) + \(\frac{28}{3R\;-\;2R}\) = \(\frac{672}{60}\)

⇒ \(\frac{28}{5R}\) + \(\frac{28}{R}\) = \(\frac{56}{5}\)

⇒ \(\frac{1}{5R}\) + \(\frac{1}{R}\) = \(\frac{2}{5}\)

⇒ \(\frac{6R}{5R}\) = \(\frac{2}{5}\)

⇒ R = 3

Speed of boat (x) and stream (y) = (3 x 3), (1 x 3)

                                                     = 9 km/hr, 3 km/hr