1. A Texas ranchman, who owned more land than he could conveniently farm, leased half of a certain field to a neighbor. This field was 2000 yards long by 1000 yards wide, but because of certain bad streaks which ran through the land it was decided that a fairer division would be obtained by cutting a band around the field than by dividing it in half. Find the width of the strip to cut around the field. [Also find the width for any L x W field.]
2. Two boys start from the same spot on the south side of a river. One boy runs due East for 250 yards, crosses the river via a bridge, then runs due North for 600 yards through a field to a flag. The other boy runs due West to a different bridge, crosses the river, then runs directly for the flag. Both boys run at the same rate and reach the flag at the same time. How far apart are the bridges?

Source: Mathematical Puzzles of Sam Loyd, Volume Two, edited by Martin Gardner, Dover Publications, New York, 1960, #90, #94.