From a Literary standpoint It may be more plausible to stop and rest. But after only half a days travel, any adventurer worth his salt would not be looking to rest. Especially if something (like nearly stepping on a trap) got the adrenaline flowing.
I dont want this to turn into an argument, but if for no other reason. I would look at this as, some people would need the rest, and some would not. Its a decision for everyone to make on there own. Not really a question of need, but of desire. Ethanius at least has a greater desire to explore than to rest.