The speed of a motion is its length of travel per unit of duration. Symbolically, speed is Δr/Δt. Pace is its duration per unit of length. Symbolically, pace is Δt/Δr. In both of these ratios, the denominator is chosen independently of the numerator. That is, the denominator is selected first, and then the numerator is measured in relation to it. The denominator may equal any positive number.
There is another way to measure motion: by comparing the measurand motion to a standard motion. Then the independent variable is from the standard motion. One can select either a length or a duration from the standard motion, and then measure a corresponding length or duration from the measurand motion.
The standard motion should be something easily reproduced, as with a clock. It may also be a maximum motion, as with the speed of light. Or it may be a minimum motion, as with a traffic jam. Whatever motion is chosen, its rate of motion is what I’ve called the modal rate.
One could then measure the speed of a motion as the ratio of its travel length per unit of length in a standard motion. Symbolically, that would be Δr/ΔR, where R equals cΔt, for example. That would have the advantage of a dimensionless ratio. Other than that, it amounts to the same thing as speed.
Similarly, one could measure the pace of a motion as the ratio of its duration per unit of duration in a standard motion. Symbolically, that would be Δt/ΔT, where T equals (1/c)Δr, for example. That would have the advantage of a dimensionless ratio. Other than that, it amounts to the same thing as pace.
Thus there are four rates of motion; symbolically, Δr/Δt, Δt/Δr, Δr/ΔR, Δt/ΔT.