A man starts walking from point A to point B at 4 km/hr. After 30 minutes, a woman starts from point A at 6 km/hr. If the woman reaches point B 20 minutes earlier than the man, then the distance between A and B in km is _________

Man walks A→B at 4 km/hr. Woman starts 30 min later from A at 6 km/hr and reaches B 20 min earlier than the man.

Let distance = $$d$$ km. Man's time = $$d/4$$ hr; Woman's time = $$d/6$$ hr. The woman starts 0.5 hr late and finishes 1/3 hr earlier, so her travel time is shorter by $$0.5 + 1/3 = 5/6$$ hr.

$$\dfrac{d}{4} - \dfrac{d}{6} = \dfrac{5}{6} \Rightarrow \dfrac{d}{12} = \dfrac{5}{6} \Rightarrow d = 10$$.