Question

The rays OM , ON , and OP in the figure, coincide at time t=0. At the same instant of time OM and OP rotate in the plane about point O in opposite directions while ON remains fixed. With respect to ON , segment OM rotates at constant rate of 3° per second and OP , at 6° per second. What is the smallest positive value of t, in seconds, for which segments OM and OP will coincide?

Answer 1

Note:

Note that the shape is a circle(s), as they all will rotate until they coincide. However, they are rotating towards each other

Step-by-step explanation:

One is rotating at 3°, while the other is rotating at 6°. We do not need to both with ON, for the question is not asking for that segment.

A circle has 360° To solve this, we must know that "the other" must complete a circle and overtake the other one.

So. First, solve for the circle (360°)

360/6 = 60

It takes one of the rays to rotate a full circle 60 seconds.

The other, at the same time, has rotated half way, as:

360/3 = 120

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Remember that one of the rays (the one that is faster), completes it's turn twice as fast. This means that you must solve for the mean:

(60 + 120)/2 = 180/2 = 90

90 seconds will be used until one overtakes the other

~Senpai