Why is there no time in the distance equation using Hubble constant, red shift and speed of light?
Are you familiar with Hubble's Law? Because this is just it, in a slightly less familiar form. 

Note that the distance in this formula is the proper distance, the distance between us and some source, not the distance travelled. 

Other than that, the speed of light in a sense defines our conception of time and space, so it is mentioned in the formula. ;)