Josh needs to cross a bridge guarded by a monsters this monster wont allow anyone to cross it will take josh at least 4 minutes to cross the bridge but the monster comes out every 3 minutes to check?

there are many variations but will give the one that seems most applicable to your question; simply run across the bridge because if it takes you 4 mins to cross it will still take time for the monster to cross even if it moves twice as fast as him, now if the ogre has a bow or is on the other side of the river josh should consider these other options , kill the monster, find another bridge, bribe the monster, wait until the monster goes for lunch or takes a dukie, swim for it, hire some ogre hookers to seduce the monster while josh runs for it, wait until the monster sleeps.