I'm working on a school project and would like to discuss some ideas. First, let's imagine that there are two lines, each line has a length x. In each line there is a "runner", so to speak, and when the runner arrives at the end, he is transported to the start point and starts to run again, infinitely. The question is: for runners a and b, is possible to define a velocity v for each runner such that the runners will never be at the same point of the line simultaneously? Is there a general formula for this, so we can make the calculations, for three, four, five, etc. runners? The second question is: if there is a general formula, is possible to use it when the lines have different lengths, for example, the first line has a length x, the second line has a length 2x, the third line has a length 3x, etc.?
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No, if they run in a loop and each have a different velocity, there are always intersection points at some time - like the minute and hour hand of a clock. – iwab Oct 16 '23 at 13:38
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Is possible to predict in which position they will intersect? Even if two runners intersect, is possible to avoid that 4 runners intersect, or 3 runners intersect, etc.? – Oct 16 '23 at 14:13