# Is it possible to determine particles' velocities from their crossings on a ring?

2 particles are constrained to move in a ring. Both particles begin moving at $t=0$ from $p=0$, each particle moving in the opposite direction of the other. It is known that they are moving at different constant velocities. Both particles pass each other (without interaction) 4 times before simultaneously returning to $p=0$.

With this information, how can I find out the ratio between the particles' respective velocities?

It seems to me that this would hold true in any case where $x:y$ is the ratio of the particles' velocities and $|x - y| = 5$. In that case, all the following would qualify: $${-2:3},\ {-3:2},\ {1:6},\ {2:7}$$

If furthermore, I know that the order of the positions where they pass is (in radians): $$\frac{4π}{5},\frac{8π}{5},\frac{2π}{5},\frac{6π}{5}$$ then can I definitively extrapolate the ratio?

Bonus points to anyone who can figure out what gave me the idea for this question in the first place.

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Did you get this question from a specific loading animation? – JoshRagem Dec 10 '12 at 14:08
Hi genghisdani - I'm adding the homework tag even though this is not actually a homework question, because it is the type that qualifies as homework-like under our policy. – David Z Dec 10 '12 at 16:09
You might try $|x - y| = 4$, instead. – WhatRoughBeast Jun 23 '15 at 23:24