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 ?
A. 13.5 km
B. 3 km
C. 15 km
D. 9 km
Answer: Option D
Solution(By Examveda Team)
Let the height of the hill = x km$$\because $$ The distance will be same man either ascend and descend
$$\frac{{x{\text{ km}}}}{{\frac{9}{2}{\text{ km/h}}}} + \frac{x}{{3{\text{ km/h}}}} = 5{\text{ hrs}}$$
\[\left\{ \begin{gathered} \because {\text{ Time = }}\frac{{{\text{Distance}}}}{{{\text{Speed}}}} \hfill \\ {\text{Total Time = Ascending}} \hfill \\ {\text{ time + Descending time}} \hfill \\ \end{gathered} \right\}\]
$$\eqalign{ & \Rightarrow \frac{{2x}}{9} + \frac{x}{3} = 5 \cr & \Rightarrow \frac{{2x + 3x}}{9} = 5 \cr & \Rightarrow 5x = 5 \times 9 \cr & \Rightarrow x = 9{\text{ km}} \cr} $$
Related Questions on Speed Time and Distance
A. 48 min.
B. 60 min.
C. 42 min.
D. 62 min.
E. 66 min.
A. 262.4 km
B. 260 km
C. 283.33 km
D. 275 km
E. None of these
A. 4 hours
B. 4 hours 30 min.
C. 4 hours 45 min.
D. 5 hours
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