Problem: a boat has to cross a river that is 1.5 km wide. There is a current of 5 km/h flowing parallel to the banks of the river. If the boat travels at 12 km/h relative to the water, what is the minimum time it will take the boat to cross the river? The fastest time will be if all of the boats speed it directed across the river, perpendicular to the current. Since horizontal motion does not affect vertical motion, it will take 1.5/12 hours (.125 hours) or 7.5 minutes to cross the river. My teacher says that this approach and the answer it yields is incorrect, but was unable to satisfactorly explain why. Her method: the resultant velocity will be 13 m/s at about 22 degrees. 1.5/cos(22) gives the distance that the boat will travel on it's journey across the river. (here is the part thst doesn't make sense to me) since the boat travels at 12 m/s relative to the water (Didnt we just agree that it would travel at 13 m/s?), it will take 1.5/cos(22)/12 hours, which equals .135 hours (8.1 minutes).