Many years later, the spider and the fly. the next generation, happen to meet in

ID: 2858180 • Letter: M

Question

Many years later, the spider and the fly. the next generation, happen to meet in an empty room of size 10' times 10' times 20'. the fly. just coming out of a calculus class, is surprised to find the spider in the room. the spider, being younger and more forthright than his father, skips all the courteous exchanges and starts immediately a hot pursuit of the fly. But he cannot catch the fly since the fly has the ability of staying in the air. Tired and disgusted, the spider retreats to a comer of the room and waits for his chance. At that moment, the fly, like a student who has just had a heavy dose of mathematics, has a sudden urge of taking a nap. With mathematics in his guts, the fly does everything in great precision. He knows that his nap will last precisely 3.56 minutes. He also knows from the chase that the spider, like its father, has a maximum speed of 8 feet per minute. With a quick computation, the fly notices that the opposite comer of the room is not far enough since the distance seems to be only Squareroot 20^2 + 20^2 = Squareroot 800 = 28.2843' away from the spider (see the figure) and the spider can reach the point in less than 3.54 minutes. But the drowsiness (as students in mathematics know well) becomes irresistible. Can you find a place in the room that the fly can make a safe nap for 3.56 minutes? I was surprised when I discovered that the point which is farthest away (if the spider is allowed to crawl only) from a comer of the room is not the opposite comer Sec if you can find a point which is farther away than the opposite corner.

Explanation / Answer

Here we will apply this formula

d= sqrt( l^2+w^2+h^2)

d= sqrt( 20^2+10^2+10^2)

d= sqrt(400+100+100)

d= sqrt(600)

d=24.5

so it the farthest distance from one corner to another

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