## Escorting Shapes

1. A police motorcyclist is escorting a 20 mile line of VIP vehicles. He drives at constant speed from his starting place at the back to the front of the line, and immediately returns with the same speed to the back of the line. He arrives at the back just as the line has moved 20 miles. How many miles did the policeman travel?
2. A destroyer is escorting a convoy of ships 20 miles long and 20 miles wide. The convoy is in the shape of a square. Starting from the rear left corner of the square, it steams to the front; then steams across the front of the square to the front right; then back down the right side and finally across the rear back to the left rear corner, arriving there just as the convoy has moved 20 miles. How many miles did the destroyer travel?
3. Same problem as previous, except the convoy is in the shape of an equilateral triangle, side length = 20. (There are three ways to consider this problem: point forward, point rear, and point side.)
4. Same problem as previous, except the convoy is in the shape of a circle.

Source: Reader Denis Borris, citing Sam Loyd for the first one. 4. Extension from Al Zimmermann and Nick McGrath independently.

Solution
Mail to Ken