A hiker has been seriously hurt somewhere in a 10-mile-by-10-mile-square area. Unable to move, he sends a distress signal with a range of two miles. When your search party is within range of his signal, your directional finder will lead you right to him. Your task is to guarantee coming within range of the hiker's signal as quickly as possible. Assume you can start from any point on the perimeter of the square and travel continuously. Your Jeep allows you to go a mile every 10 minutes.
As a warm-up problem, consider a rectangle instead of a square. Assume that the rectangle has an area of 100 square miles. To ensure finding the hiker's signal as quickly as possible, what would the dimensions of the rectangle need to be?
This article was originally published with the title Missing Hiker.