Question

Two particles start at the point (1,0) on a unit circle and move in opposite directions. The particle moving counter-clockwise is traveling with velocity 3 degree/sec. The particle moving clockwise is traveling with velocity 42 degree/sec. What is the angle corresponding to the point at which the particles will meet?

Answer 1

Let the number of degrees that the counterclockwise particles moves through be d degrees.

The number of degrees that the clockwise particle moves through will be 360-d degrees:.  The times taken to where they meet is the same for both particles.

Rate = degrees / time , so:-

3 = d/ t ;  giving   t = d/3

42 = 360- d / t so t  = (360 - d) / 42

Equating values of t:-

d/3 = (360-d) / 42

42d =  1080 - 3d

d = 1080 / 45

=  24 degrees  (answer)