A man is going away from the plane mirror with velocity of 3m/s with what velocity is he going away from his image in the mirror ?

x’ = -x, where x is position of observer and x’ is position of the image.

With mirror at 0.

So, if dx/dt = 3 m/s, dx’/dt = -dx/dt = - 3m/s.

using the classical formula for relative speed,

Vrel = dx’/dt - dx/dt = -2dx/dt = -6 m/s.

So, the image is approaching the observer at 6 m/s.