We had a sentence in one of our exercises:
Chegámos agora porque nos despachámos mais cedo
The translation underneath says
We came now because we finished earlier.
Google translate doesn’t translate despachámos in any way that is even close to finished, though.
Any ideas?
@pinnih Using the translator on this site it translated as “we dispatched” which is what I was guessing it meant. 
Yes, that’s my intuitive translation, which I can imagine also could mean we left earlier.
But the Practice Portuguese translation says: we finished earlier.
The verb despachar has several meanings and subtleties depending on context.
My 501 Verbs edition cites …to send (off), to fire ( a gun), to get rid of, (-se) to hurry (up), to get going.
So the sentence you queried “Chegámos agora porque nos despachámos mais cedo” probably best translates as " We arrived now because we hurried earlier"
Think of the English word “dispatch” which in context can mean “hurry”. You can say “do that with dispatch” when instructing someone to carry out a task quickly.
@pinnih, like @mac.cummings said, you can think of it as hurrying up and getting something done/being available earlier than planned. Dispatched is a suitable translation in other contexts (e.g. dispatching an order = despachar uma encomenda).