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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?

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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)

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