Ants on a cube

There exists a cube in space. Two ants start at two random and distinct corners of the cube and move only along the edges of the cube. If either ant is at a corner, it chooses an edge randomly and moves to an adjacent corner with uniform velocity. The ants make their decisions independently. They start moving simultaneously when the clock is at zero, and move continuously with constant speed. If it is known that an ant traverses a side of the cube in one second, find the expected time elapsed(in seconds) before they meet for the first time. Round your answer off to the nearest integer.

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