River Falls journal. [volume] (River Falls, Pierce County, Wis.) 1872-2019, 1900-09-20
Can Yon plow2 Read This.


Problem /. Two men, "An and
"B", start out to pillow a square field
of 40 acres, using Pinch plows, plow-
ing the field from the outside in. "a"
starts first, or on the outside, follow
ed by "Bn They maintain their rela-
tive positions until the field is plowed.
Question: Who plows the greater
piece, and how much? Answer: "a"
plows 2639 feet more than 3D."
Problem 1I.-Statement: given the
same conditions as to field and start
ing as In 'I', but AS team walks
faster, and after several times around
A has gone so much faster than B
he has gone once more around the
field than b and overtakes him from
behind and in this position they finish
the piece. What difference does the
fact of A having gained round on B
make with the total amounts ploWed
by each? None whatever, When the
piece is finished A has plowed 2639 TT.
more than b. Would the number of
rounds they make before A has so
gained a round on B make any differ
ence in the result? None whatayer,
whether A gains his round the first
time around or the last time, (the
329th), the result is the same.
Problem III Given the same con-
ditions as to field and starting and
blowing as in ZIP, with A at the
start going faster than B so that after
several times around A has gained
round on B and overtakes him from
behind, in which position they finish
blowing the field, as in problem I'll. !"
After so gaining round on B does A
continue to gain distance on B to the
end of the field? He does not. If he
did, then at the end the difference be-
tween what he has plowed would be
more than 2639 feet, which is impossi-
BILE. If A does not continue to gain
on b, does he from the time of gain
ing a round upon him hold his lead,
and finish the piece the same distance
He does not. If he did, then again
at the end he would be more than
2639 feet ahead of b, for the reason
that at the time OF oyertaking B, A
is ahead of him the corners so far
plowed, plus AS last round, and the
length of this last round will be great
er than the sum OF all the corners yet
TO be cut. IT, then, A does not con-
tinue to gain upon B and does not
main tain the lead he has already
gained by making one round more
than B has made and oyertaking him
from behind, does he lose ground to
the end of the field? he does. AS
stated in the last answer above, at
the time of overtaking B, A is ahead
of him the sum Of the corners so far
plowed, plus his last round, and no
matter at what part Of the field he
overtakes L his last round which he
has gained on B will be longer than
the sum Of all the corners still to be
plowed and from the time that A
overtakes B to the end Of the field, B
gains on A distance equal to the
amount by which AS last round ex-
ceeds the sum Of the corners yet to be
cut by A for B, and by his, BIS, last
round, SO that at the end A is just as
far ahead as he would have been had
he not gained the round, that is, 2639
feet, and no more.
p. S.---To make the above absolute
ly exact, on the superstition that the
blowing has been done with mathe-
NAUTICAL accuracy, there will still re-
main piece in the middle of the
field one foot square to be plowed,
and A should pillow it, thus making
his excess over B 2640 feet.