The fly and train math problem

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Discussion Overview

The discussion revolves around a mathematical problem involving two trains moving towards each other and a fly traveling back and forth between them. The focus is on calculating the total distance traveled by the fly until the trains collide, exploring different approaches to the problem, including direct calculation and infinite series summation.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents the problem and asks for the total distance the fly travels before being crushed.
  • Another participant suggests calculating the time it takes for the trains to meet as a way to find the solution.
  • A participant references a famous anecdote about John von Neumann's quick response to the problem, contrasting it with others who attempt to sum an infinite series.
  • One participant calculates that the trains will meet in five hours, leading to the conclusion that the fly travels 150 miles in that time at 30 mph.
  • Another participant expresses agreement with the calculation presented.
  • There is a reiteration of the anecdote about von Neumann, with slight variations in wording and emphasis on the simplicity of his approach.
  • One participant expresses frustration at the repetition of the anecdote within the thread.
  • A participant admits to initially solving the problem using a more complex method.

Areas of Agreement / Disagreement

Participants generally agree on the calculation of the fly's distance based on the time until the trains meet, but there are differing opinions on the approach to the problem, with some favoring direct calculation and others referencing infinite series. The discussion includes repeated anecdotes about von Neumann, indicating a lack of consensus on the preferred method of solution.

Contextual Notes

The discussion does not resolve the differences in approach to the problem, and there are varying levels of complexity in the methods discussed. Some participants express their preferences for simpler or more complex solutions without reaching a definitive conclusion.

camilus
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Ok so the problem:

2 trains are 100 miles apart traveling towards each other on the same track. Each train tavels at 10 miles per hour. A fly leaves the first train heading towards the second train the instant they are 100 miles apart. The fly travels at 30 miles per hour (relative to the ground not relative to the train he left). When the fly reaches the second train, it turns and heads back to the first train at 30 miles per hour (assume that the change in direction takes zero time). when the fly reaches the first train, he turns again. this process continues with the fly zipping back and forth between the trains as they come ever closer, until the two trains colide.

The question: How far does the fly travel until he is crushed? (total distance traveled not displacement from original position)
 
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Why don't you figure out how long it takes for the trains to meet?
 
It's also a famous anecdote
When this problem was posed to John von Neumann, he immediately replied, "xxx miles."
"It is very strange," said the poser, "but nearly everyone tries to sum the infinite series."
"You mean there's another way?" says von Neumann!
 
daveb said:
Why don't you figure out how long it takes for the trains to meet?

Well the trains will meet in five hours so if the fly flies continuously for five hours, at 30mph, he travels 150 miles.

mathematically,

[tex]d=\int \limits_0^5 30~dx=30\int \limits_0^5 ~dx = 30[x]\limits_0^5 = 30[5-0] = 150 miles[/tex]
 
Very good!
 
mgb_phys said:
It's also a famous anecdote
When this problem was posed to John von Neumann, he immediately replied, "xxx miles."
"It is very strange," said the poser, "but nearly everyone tries to sum the infinite series."
"You mean there's another way?" says von Neumann!
When I first heard this problem many years ago that how I did it. I however also realized the infinite geometric approach but it is too computational. I do not find this to be challenging problem and I am sure most will agree.
 
The way I heard it after hearing the problem, Von Neuman had the answer immediately.

"Wonderful! You must have seen the simple way! Most people take forever trying to sum the infinite series!"

"But I used infinite series."
 
Robert, that had already been told, even in this thread! I'm getting a little tired of it.
 
i did it the ugly way too the first time :(
 

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