Clocks can easily be placed on moving bodies or observers to measure travel time continuously. A moving body can have on-board devices to measure cumulative travel distance. Observers have more difficulty measuring the cumulative travel distance of an external body but it can be done by motion tracking devices. If the distance is long, multiple devices can communicate with a single system.
For theoretical physics reality is continuous so that differential equations may be used, even in quantum mechanics. This is a practical need but it also goes back to Zeno’s paradoxes: any attempt to think of reality as discrete runs into problems. So motion and measurement are continuous. Everything is a differential or a constant.
Speed is the differential dr/dt. Pace is the inverse, dt/dr. They are mutually dependent: r = r(t) and t = t(r). Their values at all points are knowable, with a partial exception for quantum uncertainty whereby one can know position but not momentum simultaneously.
Since Galileo and Newton, physics has taken time as the independent variable, which is measured first. With differentials it doesn’t matter which variable comes first. All differential equations of physics can be inverted so that length is the independent variable instead of time (duration).
Thus there are two versions of physics that are theoretically equivalent. I’ve demonstrated that by switching space and time with the equations of motion and gravity. Another way to switch space and time is to convert them with the speed of light. If the speed of light is set to one, there is minimal difference between the two versions.
The difference between the two versions of physics has more to do with culture and convention. What if the world had three dimensions of time and one dimension of space? People would think and feel about reality differently.