Unfortunately there's a fox sitting at the edge of the lake. The fox can run four times as fast as the duck can swim. If the fox catches the duck, the duck is dead. The fox can't go in the water, though.
Question 1: Can the duck get out of the lake, or is the duck doomed?
Question 2: Why?
Question 3: What's the fox-speed cutoff point for duck death? (In other words, what is the value where any faster means the fox always wins, and any lower means the duck always wins?)