A boat moves downstream at the rate of 1 km in $${\text{7}}\frac{1}{2}$$ minutes and upstream at the rate of 5 km an hour. What is the speed of the boat in the still water?

Rate downstream of boat
$$\eqalign{ & {\text{ = }}\left( {\frac{1}{{\frac{{15}}{{2 \times 60}}}}} \right)\,{\text{kmph}} \cr & = \frac{{2 \times 60}}{{15}}\,{\text{kmph}} \cr & = 8\,{\text{kmph}} \cr} $$
Rate downstream of boat = 5 kmph
Speed of boat in still water = $$\frac{1}{2}$$ (Rate downstream + Rate upstream)
$$\eqalign{ & = \frac{1}{2}\left( {8 + 5} \right) \cr & = \frac{{13}}{2} \cr & = 6\frac{1}{2}\,{\text{kmph}} \cr} $$