Runners on a Square Field

Math Puzzle

Difficulty: Medium

There is a square field of length ‘a’ (any positive real number) whose corners are A,B,C,D in the clockwise direction. Two persons started running from corners A and C along the circumference of the square field in the clockwise direction with integral speeds of v₁ and v₂.

Initially, at time t=0, distance between them is AC=√2a. Find the time t in terms of a, v₁ and v₂ when the distance between them is √2a for the next time.

Comments/Solutions are welcome.