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A takes 2 hours more than B to walk d km, but if A doubles his speed, then he can make it in 1 hour less than B. How much times does B required for walking d km ?

A takes 2 hours more than B to walk d km, but if A doubles his speed, then he can make it in 1 hour less than B. How much times does B required for walking d km ? Correct Answer 4 hours

Suppose B takes x hours to walk d km
Then, A takes (x + 2) hours to walk d km
A's speed = $$\left( {\frac{d}{{x + 2}}} \right)$$  km/hr and
B's speed = $$\left( {\frac{d}{{x}}} \right)$$  km/hr
A's new speed = $$\left( {\frac{2d}{{x + 2}}} \right)$$  km/hr
$$\eqalign{ & \therefore \frac{d}{{\left( {\frac{d}{x}} \right)}} - \frac{d}{{\left( {\frac{{2d}}{{x + 2}}} \right)}} = 1 \cr & \Leftrightarrow x - \left( {\frac{{x + 2}}{2}} \right) = 1 \cr & \Leftrightarrow x - 2 = 2 \cr & \Leftrightarrow x = 4 \text{ hours} \cr} $$

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