A girl is standing at one corner of a snowy rectangular field that measures 100 ft by 100 ft, as drawn. She wishes to reach a warm cabin located at the diagonally-opposite corner of the field. Suppose she trudges through the snow at 3 ft/sec to reach a point p at the other side of the field, then walks the remaining distance along a plowed road at 5 ft/sec to reach the cabin. In order to reach the cabin as quickly as possible, how far is point p from the cabin?.
