Setting up Lorentz transformation for two flashing lights

[cubano07]

1. The question states: "Two lights are placed along the x-axis at positions x₁ = 3.00 m and x₂ = 5.00 m. The lights flash at times t₁ = 1.00 ns and t₂ = 9.00 ns. An observer in a rest frame moving to the right sees the lights flash in the same location. Assume that the origins of the two rest frames coincide at t = t' = 0.

a) Find the speed of the observer.

b) Find the time between the flashes as seen by the moving observer.2. It says that as a hint, to think Lorentz Transformations.3. Here is where I am stuck, I have no idea how to even begin it, since I do not know whether the observer and the S' frame are both moving together, and since U_x' = U_x - v/(1-U_xv/c²) would be the speed of the observer, I do not know what U_x or v could be.

I have also tried applying a Lorentz transformation on the x positions and times and such, but my gut tells me that's dead wrong anyway. If anyone can help shine some light on this situation (pardon the pun) it would really help me a lot. Thanks

 

[Muphrid]

If both lights are supposed to flash at the same x-location in the primed coordinate system, can't you use that to deduce something about the Lorentz transformation that connects the two frames?

 

[vela]

You're making it too complicated. There's no need for the velocity-addition formula. The rest frame of the observer is the primed frame.