Rates of motion are almost always expressed as a ratio with respect to time (duration space). For example, the average speed of a body is the travel distance of the body divided by the travel time. This makes the independent variable time and distance the dependent variable.
However, there is no physical dependency of motion on time rather than distance. One could just as well express the average rate of motion as the travel time of the body divided by the travel distance. The ratios are equally valid.
This is a general result. There is a binary symmetry between length and duration. Travel distance and travel time are interchangeable as far as the equations of physics are concerned. J. H. Field has expressed this as a postulate for space-time (length-duration) exchange (STE):
(I) The equations describing the laws of physics are invariant with respect to the exchange of space and time coordinates, or, more generally, to the exchange of the spatial and temporal components of four vectors. (A four-vector has three components of length and one of distime.)
He avoids the question of 3D duration space by limiting the STE to the direction of inertial motion. Here we generalize the STE postulate to include 3D duration space:
(II) The equations describing the laws of physics are invariant with respect to the exchange of length and duration coordinates, or, more generally, to the exchange of the length and duration components of six-vectors. (A six-vector has three components of length and three of duration.)
Field found the STE to violate Galilean symmetry, but this is incorrect because duration is three dimensional, and there is a dual Galilean transformation symmetric to the Galilean transformation.
The STE postulate affirms the complete symmetry of length and duration. As distance is the metric of length space, a kind of length, so distime is the metric of duration space. The metric of length space or duration space may be used to organize events linearly, with equivalence classes defined for events at the same position in the order.