I think I just always used the medium speed, and went faster if there were robbers chasing me. Was guaranteed to win without thinking. Do the river mini-game when possible; if you try to walk across you sink almost every time. Are you trying to win without anyone dying?
I always used medium speed at the other difficulties with no problems, but my resources drain way too fast on medium speed on very hard. Trying to beat it on very hard with all your members alive will seem impossible to me because they never recover from their illness.