A spider stands on one corner of a solid wooden cube.
On the opposite corner sits a
delicious fly.
The spider can scurry across the cube’s surface at a speed of 3 inches per second. .
The fly needs 10 seconds before he can fly away (presumably to deice his wings).
What is the smallest cube for which the fly can escape in time?
The spider can travel 30 inches in 10 seconds.
The shortest path is to go to from her corner to the midpoint of one of the opposite sides of a face and from there around the edge and directly to the icy fly.
This path, if the cube is unfolded, is the hypotenuse of a right triangle of sides x and 2x. Where x is the side length of the cube.
This hypotenuse, by Pythagorean theorem is x*sqrt(5).
30/sqrt(5) = 6*sqrt(5) is about 13.4 inches.

Posted by Jer
on 20151015 09:12:14 