2D runner position relative to camera

Hi Unity Community, I am making an infinite runner/shooter 2D game. I have my player running close to left border of screen and camera follows the player. I want to change my camera settings so that when user touches and hold the screen (Fire1) he runs fast and can move close to right border of camera view and if he stops touch player again slowly slides back to left side of screen. This camera setting is implemented in Ramboat. I have my camera attached to an empty game object "CameraMan" I tried to move my camera man with same speed as my player is moving but this doesn't work as after few seconds CameraMan overtakes the player and my player is out of camera view.

I am sure there is simple approach available but I just can't think of it. I am stuck in this for a week now. Any help is much appreciated.

I hope i explained the problem well. Thanks in advance. :)