Relative Motion Questions

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of $60\text{km/h}$ in the direction X to Y notices that a bus goes past her every $30\text{minutes}$ in the direction of her motion, and every $10\text{minutes}$ in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.

Two boys are standing at the ends A and B of a ground, where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is :