1. The problem statement, all variables and given/known data This is new for me, so forgive me my clumsiness. I am working on the following problem: A particle p is moving with a velocity v1 = c (speed of light) towards an object q, which is moving in the same direction with the speed v2, where v1>v2. Now, v2 is a function of the distance r between p and q. I need to find the time when p "catches up" with q. 2. Relevant equations v2(r)= v0hr, where h - the Hubble constant, v0 - initial velocity, and r - distance between p and q 3. The attempt at a solution Particle p will "catch up" with q when the distance between them is 0, so we have: r - s =0 and r = s (1) v2(r)= v0hr Differential equation: ds/dt = v0hr Separating variables: ds/r= v0h dt Integrating: log r = v0ht + c r = ev0ht+c r = ecev0ht ec=R r=Rev0ht Plugging into (1) Rev0ht = v1t I am not sure how to proceed from here or if any of it makes sense.