Two particles in circular motion

Particles A and B are constrained to move in concentric circular paths, which are so infinitesimally close that they may be considered to be a single circular path of circumference 960 metres, along which the particles may move without touching. After starting simultaneously from two infinitesimally close points, they pass each other every 6 seconds as they both move in the same sense (clockwise or anticlockwise) at different constant speeds. Then, after starting simultaneously from two infinitesimally close points, they pass each other every 4 seconds as they move in opposite senses, with the same constant speeds as before. If Particle A is the faster moving particle, how many times faster than B does it move?

(Accelerations and decelerations may be ignored.)