Admit speeding, but don't say too much. Why would you say it was unsafe? Do you think it was? If not, leave all that out.
Don't mention anything about the radar detector (or lack there of), nothing about driving for a long time. Admit the guilt to speeding, but don't admit guilt to anything else (unsafe, tired, long drive). If you were truly keeping up with traffic, you can say that. Depends on how many people were on the road. Also, you said you were in the right lane, so that probably doesn't apply anyways.
There is a saying you may have heard: K.I.S.S.
If not, try this (its in BOLD):
http://www.acronymfinder.com/af-query.asp?String=exact&Acronym=KISS
Good Luck.
