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 |
.
...
THE SOLUTION
.
.
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. |
