u/Boring_Housing3927

I know it is too late to upload this but hear me out

In the problem the amount of momentum going to right and left must be same as the pressure in the equilibrium mixture remains constant so there can be no region in the box where the amount of momentum going one side is larger than other so even if we reverse the velocity amount of momentum going to either side remains same which will result in no change and since it does not consider any interaction with particles the momentum going one side will always be equal to other which suggests particles to go and hit either side walls

Still the reversal of speed (or you may consider time) has no flow but I wanted to know what others thought about this approach