Mr. P drove at a steady clip along the
highway, his wife beside him. "Have you
noticed," he said, "that those annoying signs
for Wild and Wonderful West Virginia seem to
be regularly spaced along the road? I wonder
how far apart they are."
Mrs. P glanced at her watch, then counted the
number of signs they passed in one minute.
"What an odd coincidence!" exclaimed Mrs. P.
"When you multiply that number by ten, it
exactly equals the speed of your car in miles
per hour."
Assuming that the car's speed is constant,
that the signs are equally spaced, and that
Mrs. P's minute began and ended with the car
midway between two signs, how far is it between
one sign and the next?
Solution to the Problem:
The curious thing about this problem
is that you do not need to know the car's
speed to determine the spacing of the signs.
Let
x be the number of signs passed in
one minute.
In an hour, the car will pass
60x signs.
The speed of the car is
10x miles per hour.
In 10x miles, it
will pass 60x/10x, or 6 signs.
The signs
therefore are 1/6 mile, or 880 feet, apart.
From: Martin Gardner's
New Mathematical
Diversions published by the M.A.A. in
1995.