How far does the fly fly in the end?

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Homework Help Overview

The problem involves two cyclists approaching each other from a distance of 20 km, each traveling at a speed of 10 km/h, while a fly flies back and forth between them at a speed of 15 km/h. The original poster is attempting to determine the total distance the fly travels before the cyclists meet.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster suggests that the fly travels 15 km based on the time it takes for the cyclists to meet. Some participants confirm this reasoning, while others introduce the idea of using the von Neumann method with varying speeds for the cyclists.

Discussion Status

The discussion includes confirmations of the original poster's reasoning, as well as suggestions to explore alternative methods for solving the problem. There is an acknowledgment of different approaches being considered, but no explicit consensus has been reached.

Contextual Notes

Participants mention the context of a calculus class and the introduction of series, indicating a potential educational framework for the problem. There is also a playful tone regarding the exploration of different methods.

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Two cyclists start cycling towards each other with an even speed of 10km/h. They start of 20km away from each other. At the same time a fly starts from one of them and flies to the other one, back to the first, and so on until they meet. How far has the fly flown in the end if it flew with a speed of 15km/h?

I'm thinking it has to be 15km, since the two guys will meet half way after 1 hour, and the fly flies 15km in one hour. Can someone confirm this?
 
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i confirm, you got it right :biggrin:
 
Just for fun, did anyone try the von Neumann method to solve the problem - with different speeds for the cyclists? :)
 
Not yet, but as you said, it should be done - just for fun.
 
Tide said:
Just for fun, did anyone try the von Neumann method to solve the problem - with different speeds for the cyclists? :)

That is exactly how my calc 2 teacher introduced us to series, starting with that question then telling the story about Von Neumann.
 

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