A takes 2 hours 30 minutes more than B to walk 40 km. If A doubles his speed, then he can make it in 1 hour less than B. What is the average time taken by A and B to walk a 40 km distance?
A. 5 hours 45 minutes
B. 7 hours 15 minutes
C. 5 hours 15 minutes
D. 6 hours
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & \frac{{40}}{A} - \frac{{40}}{B} = 2\frac{1}{2} = \frac{5}{2}{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {\text{i}} \right) \cr & \frac{{40}}{B} - \frac{{40}}{{2A}} = 1{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {{\text{ii}}} \right) \cr & {\text{Equation }}\left( {\text{i}} \right) + {\text{Equation }}\left( {{\text{ii}}} \right) \cr & \frac{{40}}{A} - \frac{{40}}{{2A}} = \frac{5}{2} + 1 \cr & \frac{{40}}{A} - \frac{{40}}{{2A}} = \frac{7}{2} \cr & \frac{{40}}{{2A}} = \frac{7}{2} \cr & A = \frac{{40}}{7} \cr & {\text{Put the value of A in equation }}\left( {\text{i}} \right) \cr & 7 - \frac{{40}}{B} = \frac{5}{2} \cr & 7 - \frac{5}{2} = \frac{{40}}{B} \cr & \frac{9}{2} = \frac{{40}}{B} \cr & B = \frac{{80}}{9} \cr & {\text{Now, required answer}} \cr & = \frac{{\frac{{40}}{{\frac{{40}}{7}}} + \frac{{40}}{{\frac{{80}}{9}}}}}{2} \cr & = \frac{{7 + \frac{9}{2}}}{2} \cr & = \frac{{23}}{4} \cr & = 5\frac{3}{4} \cr & = 5{\text{ hours }}45{\text{ minutes}} \cr} $$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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