A man can walk uphill at the rate of $$2\frac{1}{2}$$ km/hr and downhill at the rate of $$3\frac{1}{4}$$ km/hr. If the total time required to walk a certain distance up the hill and return to the starting point was 4 hr 36 min, then what was the distance walked up the hill by the man ?
A. 4 km
B. $$4\frac{1}{2}$$ km
C. $$5\frac{1}{2}$$ km
D. $$6\frac{1}{2}$$ km
Answer: Option D
Solution(By Examveda Team)
Average speed :$$\eqalign{ & = \frac{{\left( {2 \times \frac{5}{2} \times \frac{{13}}{4}} \right)}}{{\left( {\frac{5}{2} + \frac{{13}}{4}} \right)}}{\text{ km/hr}} \cr & {\text{ = }}\left( {\frac{{65}}{4} \times \frac{4}{{23}}} \right){\text{ km/hr}} \cr & = \left( {\frac{{65}}{{23}}} \right){\text{ km/hr}} \cr} $$
Total time taken :
= 4 hr 36 min
$$= 4\frac{36}{60}\,\, hr$$
$$= 4\frac{3}{5}\,\, hr$$
$$= \frac{23}{5}\,\, hr$$
Total distance covered uphill and downhill :
$$\eqalign{ & = \left( {\frac{{65}}{{23}} \times \frac{{23}}{5}} \right){\text{ km}} \cr & = 13{\text{ km}} \cr} $$
∴ Distance walked uphill :
$$\eqalign{ & = \left( {\frac{{13}}{2}} \right){\text{ km}} \cr & = 6\frac{1}{2}{\text{ km}} \cr} $$
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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