Mathematical_Recreations-Kraitchik-2e

20 Mathematical Recreations
0.65 (mile) _ 0.65 x 5,280 x 12 _ 41,184 (inches)
1 (hour) - 60 x 60 - 3,600 (seconds)
gives us our velocity. Then
D · t 41,184 625 650· h
tS ance = 3,600 x IT = mc es.
That is how far each spider traveled. But we were asked to
find the dimensions of the room. Therefore, now, let us
spread out its walls, ceiling, and floor onto a plane, much as
if we were to open out the six faces of a cardboard box to
make one flat piece. Since there are several possible paths,
this must be done in all possible ways, keeping the wall from
which the spiders start fixed, and laying down the others in
such a way as to keep every face attached to another along
a common edge. We can then see that the following eight
paths are possible:
(1) Over the floor and parts of the two end walls.
(2) Over the ceiling and parts of the two end walls.
(3) Over one side wall and parts of the two end walls.
(4) Over the other side wall and parts of the two end walls.
(5) Over the ceiling and one side wall and parts of the two
end walls.
(6) Over the ceiling and the other side wall and parts of
the two end walls.
(7) Over the floor and one side wall and parts of the two
end walls.
(8) Over the floor and the other side wall and parts of the
two end walls.
Denote the three dimensions of the room by 1 = length,
w = width, and h = height. The lengths of the various paths
may then be expressed:
Distance = 1 + h = 650 inches. (1,2)
Distance = v'160 2 + (l + W)2 = 650 inches. (3,4)