# Run to a point in a triangle in shortest time [closed]

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
If this question can be reworded to fit the rules in the help center, please edit the question.

• I'm pretty sure an answer from the previous question solves this perfectly fine using apollonian circles. – greenturtle3141 Jul 7 at 4:24
• It could be - the challenge is to do it with high school basic math. – Moti Jul 7 at 5:42
• Related and probably duplicate: Shortest time to meet – Rubio Jul 7 at 7:30
• @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. – Rubio Jul 7 at 7:34
• @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. – greenturtle3141 Jul 7 at 16:35