A man row to a place 48 km distant and back on 14 hours text. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is?

Solution (By Examveda Team)

Suppose he moves 4 km downstream in x hours.
Then, Speed downstream
$$\eqalign{ & {\text{ = }}\left( {\frac{4}{x}} \right)km/hr \cr & {\text{Speed upstream}} \cr & {\text{ = }}\left( {\frac{3}{x}} \right)km/hr \cr & \therefore \frac{{48}}{{\left( {\frac{3}{x}} \right)}} + \frac{{48}}{{\left( {\frac{4}{x}} \right)}} = 14\,\,\,or\,\,\,x = \frac{1}{2} \cr & So,\,{\text{Speed downstream}} \cr & {\text{ = 8 }}km/hr \cr & {\text{Speed uptream = 6 }}km/hr \cr & {\text{Rate of the stream}} \cr & {\text{ = }}\frac{1}{2}\left( {8 - 6} \right)km/hr \cr & = 1\,km/hr \cr} $$