Looks like an old problem(it is not)
We have three particles each of mass \(m\) namely \(A,B,C\) placed at the vertices of an equilateral triangle of side length \(l\)
At \(t=0\), \(A\) starts moving towards \(B\), \(B\) starts moving towards \(C\), \(C\) begins moving towards \(A\), each with a velocity \(v\).
Find the distance(not displacement) travelled by \(A\) from \(t=0\) till the time when all the three particles collide with each other.
Details and Assumptions
1)The velocity of A is always directed towards \(B\) and is \(v\),and similarly for the other two particles.
3)Ignore gravity and anything else.