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?

Solution (By Examveda Team)

$$\eqalign{ & \frac{{40}}{A} - \frac{{40}}{B} = 2\frac{1}{2} = \frac{5}{2}{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {\text{i}} \right) \cr & \frac{{40}}{B} - \frac{{40}}{{2A}} = 1{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {{\text{ii}}} \right) \cr & {\text{Equation }}\left( {\text{i}} \right) + {\text{Equation }}\left( {{\text{ii}}} \right) \cr & \frac{{40}}{A} - \frac{{40}}{{2A}} = \frac{5}{2} + 1 \cr & \frac{{40}}{A} - \frac{{40}}{{2A}} = \frac{7}{2} \cr & \frac{{40}}{{2A}} = \frac{7}{2} \cr & A = \frac{{40}}{7} \cr & {\text{Put the value of A in equation }}\left( {\text{i}} \right) \cr & 7 - \frac{{40}}{B} = \frac{5}{2} \cr & 7 - \frac{5}{2} = \frac{{40}}{B} \cr & \frac{9}{2} = \frac{{40}}{B} \cr & B = \frac{{80}}{9} \cr & {\text{Now, required answer}} \cr & = \frac{{\frac{{40}}{{\frac{{40}}{7}}} + \frac{{40}}{{\frac{{80}}{9}}}}}{2} \cr & = \frac{{7 + \frac{9}{2}}}{2} \cr & = \frac{{23}}{4} \cr & = 5\frac{3}{4} \cr & = 5{\text{ hours }}45{\text{ minutes}} \cr} $$