Challenge 3
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Two bicycles are 20 miles apart. They start towards each other at 10 MPH. When they start, a fly on one starts toward the other at 15MPH. When it reaches the second, it immediately turns around, and flys back to the first. The fly continues to go back and forth until the bikes meet. When the bikes meet, how far will the fly have flown. There is an easy way to solve this, and a hard way. Both yield the same answer. When Von Neuomon was posed this question decades ago, which way did he choose to solve it, and how long do you think it took him? Ed Dixon
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Two bicycles are 20 miles apart. They start towards each other at 10 MPH. When they start, a fly on one starts toward the other at 15MPH. When it reaches the second, it immediately turns around, and flys back to the first. The fly continues to go back and forth until the bikes meet. When the bikes meet, how far will the fly have flown. There is an easy way to solve this, and a hard way. Both yield the same answer. When Von Neuomon was posed this question decades ago, which way did he choose to solve it, and how long do you think it took him? Ed Dixon
15 miles... better yet 24.15 km ;) -Ben "My mind tends to wander, but being a small mind, it never wanders very far." - Dave Marinaccio [All I really need to know I learnt from watching Star Trek.]
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Two bicycles are 20 miles apart. They start towards each other at 10 MPH. When they start, a fly on one starts toward the other at 15MPH. When it reaches the second, it immediately turns around, and flys back to the first. The fly continues to go back and forth until the bikes meet. When the bikes meet, how far will the fly have flown. There is an easy way to solve this, and a hard way. Both yield the same answer. When Von Neuomon was posed this question decades ago, which way did he choose to solve it, and how long do you think it took him? Ed Dixon
The bikes take 1 hour to meet. In one hour the fly flies 15 miles. This of course assumes that each of the bikes is traveling at 10mph making the speed of closure 20mph, if the closure speed is 10mph (each bike traveling at 5mph), then the fly would fly 30 miles.
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Two bicycles are 20 miles apart. They start towards each other at 10 MPH. When they start, a fly on one starts toward the other at 15MPH. When it reaches the second, it immediately turns around, and flys back to the first. The fly continues to go back and forth until the bikes meet. When the bikes meet, how far will the fly have flown. There is an easy way to solve this, and a hard way. Both yield the same answer. When Von Neuomon was posed this question decades ago, which way did he choose to solve it, and how long do you think it took him? Ed Dixon
>Two bicycles are 20 miles apart. They start towards each other at 10 MPH. Let's introduce a new coordinate system wich moves with bicycle 1. In this system bicycle 2 moves witch a relativ speed of 20 MPH toward bicycle 1. The distance to move remains unchanged. Hence: the bicycle 2 needs 1h to meet bicycle 1. >When they start, a fly on one starts toward the other at 15MPH It doesn't matter in wich direction the fly flies. It only matters how long the fly is "on air" and this is 1h (see above). Hence the bird flies 15 Miles away Correct? Max
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The bikes take 1 hour to meet. In one hour the fly flies 15 miles. This of course assumes that each of the bikes is traveling at 10mph making the speed of closure 20mph, if the closure speed is 10mph (each bike traveling at 5mph), then the fly would fly 30 miles.
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The problem is not hard at all. However, it will be interesting to figure out which direction the fly is facing when the two bicycles finally meet at the end of the hour :-) And how many times has the fly changed its directions during this one hour :-)
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As the fly travels an infinite number of segments in the hour, it is not possible to determine final direction. Ed Dixon
Wouldn't the fly be in fact turning !
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Wouldn't the fly be in fact turning !
Yes!!! The following is from my 7 year old son's Chinese textbook: A cow walks 5 steps to the east, then walks 5 steps to the south, then 5 steps to the west, then 5 steps to the north. Which direction is the cow's tail pointing to? If you answered south you would be wrong. The cow's tail is always pointing down!
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Two bicycles are 20 miles apart. They start towards each other at 10 MPH. When they start, a fly on one starts toward the other at 15MPH. When it reaches the second, it immediately turns around, and flys back to the first. The fly continues to go back and forth until the bikes meet. When the bikes meet, how far will the fly have flown. There is an easy way to solve this, and a hard way. Both yield the same answer. When Von Neuomon was posed this question decades ago, which way did he choose to solve it, and how long do you think it took him? Ed Dixon
The easy way is that if the bikes travel at 10MPH, they meet in 1 hour. Since the fly travels at 15MPH, it travels a total of 15 miles. The hard way is to notice that the fly is flying a series of trips, each shorter than the last. In math terms, this is an infinite series. You formulate the equations, set the variables based on the speed and distances. The result is a geometric series. The equations for a geometric series are somewhat standard, and when you plug in the values, sure enough the sum is 15 miles. Decades ago, Readers Digest published this puzzle. A student read it and shortly later spoke with Von Neumann at a cocktail party. He posed the problem to him. Von Neumann thought for a second or two and said 15 miles. The student responded that most mathematicians did not solve it the easy way, but sought the infinite series approach. Von Neumann quickly interrupted him, and said something like "Yes, and the equation is xxx, the terms are yyy, and the result is 15 miles. What is your point?". The story illustrates just how brilliant this fellow really was! Ed Dixon