A small boat is headed for a harbor 32 km northwest of its current position when it is suddenly engulfed in heavy fog. The captain maintains a compass bearing of northwest and a speed of 10 km/h relative to the water. Three hours later, the fog lifts and the captain notes that he is now exactly 4.0 km south of the harbor. 

(a) What was the average velocity of the current during those three hours? 

(b) In what direction should the boat have been heading to reach its destination along a straight course? 

(c) What would its travel time have been if it had followed a straight course?