A person, who can walk down a hill at the rate of $$4\frac{1}{2}$$ km/hr and up the hill at the rate of 3 km/hr. He ascends and comes down to his starting point in 5 hours. How far did he ascend ?

Let the height of the hill = x km
$$\because $$ The distance will be same man either ascend and descend
$$\frac{{x{\text{ km}}}}{{\frac{9}{2}{\text{ km/h}}}} + \frac{x}{{3{\text{ km/h}}}} = 5{\text{ hrs}}$$

\[\left\{ \begin{gathered} \because {\text{ Time = }}\frac{{{\text{Distance}}}}{{{\text{Speed}}}} \hfill \\ {\text{Total Time = Ascending}} \hfill \\ {\text{ time + Descending time}} \hfill \\ \end{gathered} \right\}\]

$$\eqalign{ & \Rightarrow \frac{{2x}}{9} + \frac{x}{3} = 5 \cr & \Rightarrow \frac{{2x + 3x}}{9} = 5 \cr & \Rightarrow 5x = 5 \times 9 \cr & \Rightarrow x = 9{\text{ km}} \cr} $$