1. The problem statement, all variables and given/known data The space and time coordinates of two events as measured in a frame S are as follows: Event 1: x1 = x0, t1=x0/c Event 2: x2 = 2x0, t2=x0/2c Show that there exists an inertial frame in which these events occur at the same time, and find the velocity of this frame relative to S. 2. Relevant equations Lorentz Transformations dx = k(dx' + vdt') and dt = k(dt' + vdx'/c^2) (I'm writing delta as d and gamma as k as I can't do the symbols here) 3. The attempt at a solution Now I'm pretty sure that the v is the velocity of frame S' relative to S? So I used these equations, and made the second one c^2dt/v = k(c^2dt'/v + x') Subtracting the first equation from this gives: c^2dt/v - dx = kc^2dt'/v + kdx' - kdx' - kvdt' But if the two events are simultaneous in S', then dt'=0. so c/2v = 1 v/c = 0.5 beta = 0.5 Unfortunately the answer is -0.5, which is important later in the question, and I cannot work out why. I'm sure the equations are right, and surely the v in that is the velocity of S' relative to S, which is what I'm after here? Thanks!