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

Question

Many years later, the spider and the fly, the next generation, happen to meet in an empty room of size 10' x 10' x 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 corner 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 corner of the room is not far enough since the distance seems to be only sqrt(20^2 + 20^2) = sqrt(800) = 28.2843' away from the spider and the spider can reach the point in less than 3.54 minutes. But the drowsiness becomes irresistible. Can you find a place in the room that the fly can make a safe nap for 3.56 minutes? Comments: I was surprised when I discovered that the point which is farthest away (if the spider is allowed to crawl only) from a corner of the room is not the the opposite corner. Can you can find a point which is farther away than the opposite corner?

Explanation / Answer

The fly can stay at opposite corner on the ceiling not on the floor, as fly has ability of staying in the air.

Then, the fly would be sqrt(20^2+20^2+10^2) = sqrt(900) = 30 feet away from the spider.

Time taken by spider to reach to fly = 30/8 = 3.75min.

hence, fly can complete a nap which is of just 3.56 min.

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