Two men, $A$ and $B$, set out from town $M$ to town $N$, which is $15$ km away. Their walking speed is $6$ km/hr. They also have a bicycle which they can ride at $15$ km/hr. Both $A$ and $B$ start simultaneously, $A$ walking and $B$ riding a bicycle until $B$ meets a pedestrian girl, $C$, going from $N$ to $M$. Then $B$ lends his bicycle to $C$ and proceeds on foot; $C$ rides the bicycle until she meets $A$ and gives $A$ the bicycle which $A$ rides until he reaches $N$. The speed of $C$ is the same as that of $A$ and $B$. The time spent by $A$ and $B$ on their trip is measured from the moment they started from $M$ until the arrival of the last of them at $N$. a) When should the girl $C$ leave $N$ for $A$ and $B$ to arrive simultaneously in $N$? b) When should $C$ leave $N$ to minimize this time?