This is probably one of the more counter-intuitive simple calculations you can do in physics.

In special relativity, distance is given by:

  ds^2 = dx^2 + dy^2 + dz^2 - (c^2)dt^2

  dX^2 = dx^2 + dy^2 + dz^2

Further, your velocity is given by dX/dt. If you are traveling at the speed of light, you have:

  dX/dt=c

  dX^2 = (c^2) dt^2

  dX^2 - (c^2) dt^2 = 0

  ds^2 = 0

> just curious... does "time" have a "speed" ?

It is not clear how to parse this question. Traditional "speed" is defined as distance over time. We can give this meaning for time itself by realizing that there is no single notion of time in relativity. As such, you could consider the line parallel to the time axis in the coordinate system of observer A. Since dt=0 in the coordinates of observer A, the speed of this line is not well defined. However, we could consider the coordinates of observer B. Assuming B is moving relative to A, he would see this line as being slanted, with both a time component, and a space component. As such, B could compute the speed of this line as dX'/dt', where X' is the total displacement along B's 3 spatial dimensions, and dt' is the displacement in B's time dimension. As such, B could meaningfully answer "what is the speed of A's time". Assuming I didn't mess up on the math, dX'/dt' turns out to be the velocity of A relative to B. This is a curious result that I have never seen before, but I can't really see any physical significance to it.

B could also compute dt/dt', where t' is the time axis in B's coordinate system. This computation seems more useful as it gives a direct measure of time dilation. Unsurprisingly, it also works out to be the Lorentz factor.

- Time relative to an observer: Designating a non-accelerating massive object ("observer"), you get a coordinate system which assigns a time and distance to each event (point in spacetime). In this coordinate system, the observer moves along the time axis.

- Proper time: For an object taking any path through spacetime, you can measure the "subjective" time which has passed between two points on its trajectory.

The two notions coincide along the path of an observer: For each second of subjective time, the observer moves one second along the time axis in its coordinate system. Observer time moves at one second per second, if you will.

What you usually call "velocity" is distance/time in the coordinate system of some observer. For massive objects, this is always smaller than the speed of light. If you want, you can define another notion of speed, to illustrate the original commenter's point: distance in some coordinate system per proper time. This can be arbitrarily high, because at high velocities the proper/experienced time becomes shorter.

To get back to the speed of time: If you measure coordinate distance per proper time, it is only natural to also measure coordinate time per proper time. If you take earth as the observer and follow a spaceship, this is earth time per spaceship time. For a fast spaceship, time on board passes slower than on earth (time dilation), so reciprocally, the spaceship moves through (earth) time faster than 1s/s.

(Unfortunately, the notion of proper time becomes useless for massless particles moving at the speed of light: proper time along their trajectory is constant. They "do not experience time".)