A man is standing on a rock in the middle of a circular lake of radius 1. There is a tiger on the shore of the lake that can run four times as fast you can swim, however the tiger can not swim. The tiger is hungry and always attempts to keep the distance between the two of you at a minimum.
How can you safely swim to shore?
My brother Mathews sent me the following which I now offer as a possible solution to today's dilemma:
I think you can swim to shore. I didn't do the arithmetic right earlier. Since I'm doing absolutely nothing at the moment, let me outline the solution. If no one else has this tomorrow, feel free to post.
1. Get into the water on the opposite side of the
island from the tiger. We'll assume that the unit of distance is one mile, the radius of the lake.
2. Swim towards the shore AND in the same lateral
direction as the tiger is moving, keeping the
island between you and the tiger. i.e. if the tiger begins walking clockwise to get near you, swim clockwise as well, keeping as close to the
imaginary diameter line that has the tiger as an end point. This line will move, much like the second hand on a clock and as you swim towards it your path will form a spiral.
3. At one quarter speed of the tiger, you can
cover a longer arc, in terms of degrees per unit time, until you are 1/4 mile from the island. At 1/4 mile, the circumference of your swimming circle is 1/4 that of the lake shore so both you and the tiger can complete a circle in the same
unit of time. You can keep the tiger exactly opposite the island from you by swimming parallel to the shore, but you will no longer make any progress towards shore AND keep the tiger opposite you and the island.
4. Take a deep breath.
5. Turn and swim directly toward shore as fast as
you can. You have to cover 3/4mile to get to the shore. The tiger needs to cover half the circumference of the circle, or pi*1 mile = 3.1417 miles. The tiger runs 4 times faster than you can swim, so in the time it takes you to cover 3/4 mile, he can cover 3 miles. That leaves him somewhat less than .15 miles away when you reach shore.
6. At this point, you're on your own.
A Suggested Solution
