Ants math problem

From the point of view of an ant (any of them obviously), at any instant the speed of the ant you are following is orthogonal to your own speed. The relative speed simply is... your own speed (speed vector is not the same because of direction but its norm is the same).
Which means you will close the gap in the exact same time as if the ant you are following was not moving.
So the length of the spiral every ant walks is the side of the table.

Using the symmetry of this problem (all ants are similar) one can infer that we can yield coordinates of the next anth by rotating corrdinates of the previous. Using this we can easy recieve following equations (in polar coordinates, origin in the centre of table)

Solution of this system is logarithmic spiral, it is not relevant for this problem because we can use first equation to obtain the time before they meet (when r=0, initial r is sqrt2/2*a)

where V-velocity of ants.