Arithmetic

Time, Speed & Distance

Medium

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 ___

Entered answer:

✅ Correct Answer: 10

Let the distance from $A$ to $B$ be $d$ km.

Time taken by the man $= \dfrac{d}{4}$ hours.

Time taken by the woman $= \dfrac{d}{6}$ hours.

The woman starts $30$ minutes (i.e., $\dfrac{1}{2}$ hr) later, and finishes $20$ minutes (i.e., $\dfrac{1}{3}$ hr) earlier.

So the woman spends $\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{5}{6}$ hour less on the road than the man.

$\dfrac{d}{4} - \dfrac{d}{6} = \dfrac{5}{6}$

$\dfrac{d}{12} = \dfrac{5}{6}$

$d = 10$ km.

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