Special Relativity - 2 observers - 2 frames of reference

[kachilous]

Homework Statement

An observer in frame S standing at the origin observes two flashes of colored light separated spatially by Δx = 2300 m. A blue flash occurs first, followed by a red flash 5 µs later. An observer in S ' moving along the x-axis at speed v relative to S also observes the flashes 5 µs apart and with a separation of 2300 m, but the red flash is observed first. Find the magnitude and direction of v.

Homework Equations

I believe the necessary equation is v = Δx/Δt

The Attempt at a Solution

So I initially thought I would simply have to plug into the above equation Δx = 2300 m and Δt = 5 μs. But now I am realizing that would not give me the velocity of the observer.
To find the velocity of the observer would I have to know the distance he traveled?
And then use Δt = 5x10^-6?

 

[HallsofIvy]

You titled this "special relativity" but you haven't used any formulas from relativity.

 

[kachilous]

I figured I could use x = γ(x^' + vt^') {The lorentz equation for distance}
And then since I am given the spatial separation Δx,
Δx = γ(x_o^' + vt₂^' - γ(x_o^' + vt₁^'
Then I could solve for v, but that still did not work