This is a generalization of a puzzle that dealt with an equilateral triangle.

Assume three runners with the following speeds - 4.5, 6.2, and 8.7 meters/sec. They are at the corners of a triangle with sides lengths of 75, 49, and 63 meters.

They need to decide how to select the corner for each runner and a point in the triangle to which they run simultaneously and reach it at the same and shortest time.

Only compass and unmarked ruler could be used to derive a solution.


closed as off-topic by Rand al'Thor, Glorfindel, Florian F, greenturtle3141, Rubio Jul 7 at 22:57

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – Rand al'Thor, Glorfindel, Florian F, greenturtle3141, Rubio
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  • $\begingroup$ I'm pretty sure an answer from the previous question solves this perfectly fine using apollonian circles. $\endgroup$ – greenturtle3141 Jul 7 at 4:24
  • $\begingroup$ It could be - the challenge is to do it with high school basic math. $\endgroup$ – Moti Jul 7 at 5:42
  • $\begingroup$ Related and probably duplicate: Shortest time to meet $\endgroup$ – Rubio Jul 7 at 7:30
  • 1
    $\begingroup$ @Moti This seems like it's just a math problem. Is there some specific solution you have in mind that has elements of a puzzle, not just a math problem? If not, this is going to be off-topic. $\endgroup$ – Rubio Jul 7 at 7:34
  • $\begingroup$ @Moti We're running into the same problem here - you can't just impose a "use basic geometry" condition because a) It was not stated in the question explicitly, and b) "basic geometry" is completely subjective. $\endgroup$ – greenturtle3141 Jul 7 at 16:35

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