Triangle Convergence Kinematics

Three points are located at the vertices of an equilateral triangle whose side equals 6 m. The points all start moving simultaneously with constant speed 2 m/s (their velocities, however, are changing). The first point heads continually for the second, the second for the third, and the third for the first. How soon (in seconds) will the points converge?

This problem is from one of I.E. Irodov's books and I thought it was really great; if people enjoy it, I'll post the next one as well which is sort of related but a little more complicated.

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