A boat takes total 20 hours to cover 102 km in downstream and 63 km in upstream.  The spent to cover 34 km downstream is equal to the time taken to cover 24 km in still water.  Find the speed of boat (in km/h).

9

Speed of boat = x, speed of stream = y

\(\frac{34}{x + y}\) = \(\frac{24}{x}\)

\(\frac{x + y}{x}\) = \(\frac{17}{12}\)

\(\frac{x}{y}\) = \(\frac{12}{5}\)  Let x = 12K and y = 5K

\(\frac{102}{17K}\) + \(\frac{63}{7K}\) = 20

\(\frac{6}{K}\) + \(\frac{9}{K}\) = 20

\(\frac{15}{K}\) = 20

K = \(\frac{3}{4}\)

Speed of boat ⇒ 12K = 12 × \(\frac{4}{3}\)

                               = 9 km/h