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Subj:.....The Ferry Boat Problem (S642)
From the book
"More Mathematical Puzzles of Sam Loyd"
Edited by Martin Gardner
From: Dover Publications in 1960

What is the exact width of the Hudson River?

Two ferry boats start moving at the same instant from
opposite sides of the Hudson River, one boat going fron
New York to Jersey City and the other going from Jersey
City to New York.  One boat is faster than the other,
so they meet at a point 720 yards from the nearest shore.

After arring at their destinations, each boat remains ten
minutes in the slip to change passengers; then it starts
on its return trip.  The boats again meet at a point 400
yards from the other shore.  What is the exact width of
the river?

The problem shows how the average person, who follows the
cut-and-dried rules of mathematics, will be puzzled by a
simple problem that requires only a slight knowledge of
elementary arithmetic.  It can be explained to a child,
yet I hazard the opinion that ninety-nine out of every
hundred of our shrewdest businessmen would fail to solve
it in a week.  So much for learning mathematics by rule
instead of common sense which teaches the reason why!

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 Finger pointing down from darrell94590 on 1/2/2006
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 Drawing from Ripleys-Believe It Or Not
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THE SOLUTION

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When the ferry boats meet at point "X" (see above diagram)
they are 720 yards from one shore.  The combined distance
that both have traveled is equal to the width of the river.
When they reach the opposite shore, the combined distance
is equal to twice the width of the river.  On the return
trip they meet at point "Z" after traveling a combined
distance of three times the width of the river, so each
boat has gone three times as far as they had gone when they
first met.

At the first meeting, one boat had gone 720 yards, so when
it reaches "Z" it must have gone three times that distance.
or 2160 yards.  As the diagram shows, this distance is 400
yards more than the river's width, so all mathematical work
we are obliged to do is to deduct 400 from 2,160 to get the
river's width.  It is 1,760 yards which is exactly one mile.

The amount of time each ship consumed at the landing does
not affect the problem.

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