Question : 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?
Option 1: 7 hours 15 minutes
Option 2: 5 hours 45 minutes
Option 3: 6 hours
Option 4: 5 hours 15 minutes
Correct Answer: 5 hours 45 minutes
Solution :
Let the speed of A as $a$ km/hr and the speed of B as $b$ km/hr.
$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$
From the problem,
A takes 2 hours 30 minutes more than B to walk 40 km.
$⇒\frac{40}{a} = \frac{40}{b} + \frac{5}{2}$
If A doubles his speed, he can make it in 1 hour less than B.
$⇒\frac{40}{2a} = \frac{40}{b} - 1$
Solving these two equations simultaneously,
$⇒a = \frac{40}{7}$ km/hr
$⇒b = \frac{80}{9}$ km/hr
The time taken by A to walk 40 km = $\frac{40}{a}$ = 7 hours
The time taken by B to walk 40 km = $\frac{40}{b}$ = 4.5 hours
So, the average time taken by A and B to walk a 40 km distance = $\frac{7 + 4.5}{2} = \frac{11.5}{2}$ = 5.75 hours or 5 hours and 45 minutes.
Hence, the correct answer is '5 hours and 45 minutes'.
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