Special Relativity - "Simultaneity"

[FaraDazed]

Homework Statement

An experimenter triggers two lights simultaneously, which produces a
large flash located at the origin of his reference frame and a small one at x = 23.8 km.
An observer, who moves with speed 0.374c in the positive x direction, also views the
flashes. What is the time interval in seconds between them, according to her (the observer)?

Homework Equations

$\Delta t = \gamma (\Delta t' + \frac{v \Delta x'}{c^2})$

The Attempt at a Solution

I have use the equation above and got an answer. However, if I am correct, I do not fully understand it, and the question also asks us to clearly explain each step of our solution, so would appreciate some advice/help with that. And if I am not correct then I would appreciate if someone could point out what I did wrong and any feedback.

I used the above equation, and because of the way the question is worded I assume that t' is zero, i.e. according to the experimenter there is no time between the flashes so then the above equation becomes...
$$\Delta t = \gamma (\frac{v \Delta x'}{c^2}) \\ \Delta t = \frac{c^{-2}v \Delta x'}{\sqrt{1-\frac{v^2}{c^2}}} \\ \Delta t = \frac{(3 \times 10^8)^{-2}(0.347 \times 3 \times 10^8) (23800)}{\sqrt{1-\frac{(0.347 \times 3 \times 10^8)^2}{(3 \times 10^8)^2}}} = 2.935 \times 10^{-5} s = 29.35 \mu s$$

Thanks :)

 

[Chestermiller]

Looks good, although that Δx should be a Δx'.

Chet

 

[FaraDazed]

Looks good, although that Δx should be a Δx'.

Chet

Thanks :) Ah yes, I typed it up wrong once and then copied and pasted it through the calculation . I've gone back and changed it now :).