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John and Peter are two friends living in two nearby villages 15km apart.
One day they arrange to meet, but little do they know, a “flies marathon flyer”, an irritating fly, decides to play a game.
John walks with 7km/h speed. Peter walks with a 8km/h speed.
The fly flies at a 13.125 km/h speed.
If they all start moving together, and the fly moves between each other's nose back and forth, can you find how long a “flies marathon” is?

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    $\begingroup$ I enjoyed answering this puzzle. It is a shame someone has marked it as a duplicate - the other question referenced only involves 2 moving parties, whereas this one uses 3. I understand that the method and logic to solve them might be the same, but you could say that about any mathematical puzzle. $\endgroup$ – Astralbee Nov 26 '18 at 10:26
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    $\begingroup$ This is an old classic puzzle. There is a story about John von Neumann's encounter with this puzzle in the 1920s. $\endgroup$ – Jaap Scherphuis Nov 26 '18 at 12:24
  • $\begingroup$ @Astralbee the puzzle-worthy parts are identical in both cases. The only differences are in the boring subtraction and addition bits of the setup. $\endgroup$ – Bass Nov 27 '18 at 19:18
  • $\begingroup$ @Bass I wasn't aware it was a "classic" puzzle. If the OP shamelessly copied it then fair enough, it shouldn't be here. I just think there are so many variations on puzzles that are essentially the same - like the "only one of these people is telling the truth" puzzles. Once you know the logic of one, you can solve them all. Same here. $\endgroup$ – Astralbee Nov 28 '18 at 9:43
  • $\begingroup$ @Astralbee the puzzle being closed as a dupe has nothing to do with copying, shamelessly or otherwise. It's just that the site consensus has decided that it's better to have each puzzle here once, and only once. (If you don't think that's a good idea, you might want to bring it up on the meta, that's how this site's policies get better over time.) $\endgroup$ – Bass Nov 28 '18 at 12:31
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The marathon is:

13.125 km.

Because:

After 1 hour Peter will have walked 8km, John will have walked 7km. 8+7=15, so as they are 15km apart, they will meet in the middle at exactly 1 hour. The fly flies at 13.125km/h so that's how far it can fly in any direction before they all meet. Because the fly is flying back and forth for as long as the other two are walking there is no need to calculate where along the journey it will meet the two or how often.

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