What is the motion of K' in the direction of the x-axis?

[xWaffle]

Homework Statement

Find a system K' in which the following events in frame K appear at the same time:

i) x₁ = a; t₁ = (2a) / c; y₁ = 0; z₁ = 0
ii) x₂ = 2a; t₂ = (3a) / (2c); y₂ = 0; z₂ = 0

Describe the motion of K'.

Homework Equations

Lorentz transformations; time dilation; length contraction..maybe?

The Attempt at a Solution

My scratch-work is too complicated to try and re-post here, but basically I have come to the conclusion I don't really know how to use the equations to describe the motion of K'. I need to describe the motion of K' in the direction along which the motion occurs, which is obviously the x-axis

 

[voko]

What is the time of any event in K as seen in K'?

 

[xWaffle]

In K the event is seen as T0 = t2 - t1 = (3a / 2c) - (2a / c), and in K'.. um, T' = gamma*T0? If that's so then I don't know how to calculate this because gamma relies on velocity which is what I'm trying to find

 

[voko]

No, it is not gamma*T0 in K'. What is the Lorentz transformation of the temporal coordinate?