Ken's POTW
Two Fields

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.]

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.
Solution
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