According to TOS: "That Which Survives" the Enterprise covered 1000 lightyears in 12 hours at warp 8.4. They would have made Voyager's journey in about a month. They also made it as far as the rim of the galaxy ("Were No Man...") and the centre twice ("Megas Tu" and STV, the latter explicitly launching from Earth)
Trek writers just pull the numbers out of thin air for time, distance and speed. It's speed of plot. They never use the charts or formulas in the technical manuals.