Spatial Variation in the time between when two signals are received

[dsdsuster]

This #94 from the 2008 GRE:

An observer O at rest midway between
two sources of light at x = 0 and x = 10 m
observes the two sources to flash simultaneously.
According to a second observer O′, moving at a
constant speed parallel to the x-axis, one source of
light flashes 13 ns before the other. Which of the
following gives the speed of O′ relative to O ?

Answer: .36c

By using a lorentz transformation I find the 10m event always happens earlier in the O' frame by gamma*v*(10m)/c^2. However, I find that the actual amount of time between when observer O' receives the two signals is dependent on the location of the observer O' when the signals are emitted, in the spatial interval between the two signal sources.

Can anyone corroborate or refute this claim? I recover the correct answer when I assume the observer O' is halfway in between the signals when they are emitted in O. The question's construction seems to imply that there is answer independent of where O' is.

Appreciate the help!

 

[mfb]

However, I find that the actual amount of time between when observer O' receives the two signals is dependent on the location of the observer O' when the signals are emitted, in the spatial interval between the two signal sources.

That is correct, but it is not relevant for the problem.
The question does not ask about the times O' receives the light pulses, but the calculated flashing time difference (based on the received light pulses and the calculated distance to their origin).

 

[dsdsuster]

Thanks mfb,

What I'm saying is that the time interval between reception of signal A and reception of signal B is dependent on O' 's location. An intelligent observer could deduce the time interval between when the two signals are emitted and this interval as you say is dependent only on O' 's velocity.

The question is however asking for the first of what I mentioned if I'm reading it correctly?

 

[mfb]

What I'm saying is that the time interval between reception of signal A and reception of signal B is dependent on O' 's location. An intelligent observer could deduce the time interval between when the two signals are emitted and this interval as you say is dependent only on O' 's velocity.

Right.

The question is however asking for the first of what I mentioned if I'm reading it correctly?

I think it asks for the second.

 

[dsdsuster]

Hmm, I think you're probably right now. Thanks for your help.