AB:
CDE
CED
DCE
DEC
ECD
EDC
combinations starting AB? 6. Combinations starting AC? 6. Combinations starting AD? 6. Combinations starting AE? 6
combinations starting A? 6+6+6+6= 24.
combinations starting B? 24
C? 24
D? 24
E? 24
5x24= 120. 120 combinations= 120 trips
2 trips per week (there and back)= 60 weeks. right? unless i made a mistake
omg you're too good sputnik. check out my post I edited a few minutes ago

your final answer is not totally correct, but that's a mistake of my part.
they stay in the same combination (there and back), i forgot to mention that, so its 120 weeks and not 60, but actually that's what you calculated! well done!
is anyone up for a new riddle?