A boat moves downstream at the rate of 1 km in 7¹/₂ minutes and upstream at the rate of 5 km an hour. What is the speed of the boat in the still water?

Explanation:-

$$\eqalign{ & {\text{Downstream = }} \cr & \left( {{\text{Distance}}} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {{\text{Time}}} \right) \cr & {\text{1 km}}\,\, - - - - - - - > \,7\frac{1}{2}{\text{ min}} \cr & \downarrow \times {\text{8}}\,\, < - - - - - - - \,\,\, \downarrow \times {\text{8}} \cr & {\text{8km}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{60min(1 hour)}} \cr & {\text{Upstream = }} \cr & {\text{5km 1 hour of speed}} \cr & {\text{Seep of the boat in still water }} \cr & {\text{ = }}\frac{{\left( {{\text{Downstream + Upstream}}} \right)}}{2} \cr & = \frac{{8 + 5}}{2} = \frac{{13}}{2} = 6\frac{1}{2}\,{\text{km/h}} \cr}$$