Two athletes time compensation

[Andremag12]

Homework Statement

In a reference system S two athletes are aligned at a distance d relative to each other on the Y axis to make a run parallel to the x axis. Two starters, one next to each athlete, shoot their guns out at slightly different times, offsetting the advantage of better athlete. The time difference in S is delta T. For which time difference there will be a reference system S 'in which there is not compensation, and which time difference there is a reference system S' in which there is a real compensation ?.
Determine explicitly the Lorentz transformation that leads to S' suitable for each of the possibilities listed above, calculating the speed of S' to S and the space-time positions (events) of each athlete in the S system.

Homework Equations

Lorentz tranformation Equation

The Attempt at a Solution

I don´t really understand the exercise, but firs I think you must asume that the coordenates of one of the athletes are at the origin, and the other has the displacement d.
r1=(ct1,0,0,0)
r2=(ct2, d,0,0)

When you have two events ussually you use the space time interval

(delta S)^2 =(ct2-ct1)^2-(x2-x1)^2-(y2-y1)^2-(z2-z1)^2

But i don't understant what it means no compensation real compensation?

 

[PeroK]

I don't understand the question either. I think it's asking for a frame where the starting guns fire simultaneously, but the rest is confusing.

 

[Andremag12]

I don't understand the question either. I think it's asking for a frame where the starting guns fire simultaneously, but the rest is confusing.

Maybe there are some problem with translation, the problem is in spanish, but I agree, if there is no compensation from S' the two starting guns fire simultaneously, so delta t must be zero. So

Δs^2 < 0
But how I show this?

 

[PeroK]

Maybe there are some problem with translation, the problem is in spanish, but I agree, if there is no compensation from S' the two starting guns fire simultaneously, so delta t must be zero. So

Δs^2 < 0
But how I show this?

I'm going offline now but perhaps someone else can help.

You need to think of your starting coordinates and what direction S' needs to move.