We propose the concept of relative translation gains, a novel Redirected Walking (RDW) method to create a mutual movable space between the Augmented Reality (AR) host's reference space and the Virtual Reality (VR) client's space. Previous RDW methods have focused on maximizing the movable space at the expense of aligning the coordinates between the AR and VR side, and could only be applied to collaborative scenarios involving sequential tasks. Our method solves these problems by adjusting the remote client's walking speed for each axis of a VR space to modify the movable area without coordinate distortion. We estimate the relative translation gain threshold, defined as the extent to which the walking speed can be altered without creating a perceived difference in distance. In order to reflect features of the reference space in generating the mutual space, we then examine how changing its size affects the threshold value. Our study showed that for remote clients connected to the larger reference space, relative translation gains can be increased to utilize a VR space bigger than their real space. Our method can be applied to create optimal mutual spaces for a wider variety of asymmetric Mixed Reality (MR) remote collaboration systems.