I am studying for an exam on Special Relativity, and I made a toy problem to practice, but I ended up confusing myself. I know something is wrong with my intuition, but can someone please point where I am making the error? Here's the problem:

Consider a rocket traveling with along the x-axis with constant velocity 0.8c. At some time t0=0, the rockets starts a clock and emits a photon. At t1=0.6s he stops the clock. What is the separation between the rocket and the photon for the rockets reference frames, and for a reference frame at rest?

Here's my work: okay so from the reference frames of the rocket, the rocket appears to be at rest, so the separation would be the distance the photon travels: 0.6*3*10^8 = 1.8*10^8m

From a stationary rest frame we find

γ = 1/√(1-0.8^2) = 1/0.6

t1 = t1'*γ = 1 = 1s

The rocket is moving at 0.8c so it travels 0.8*3*10^8 = 2.4*10^8m

The photon travels 3*10^8m

So the separation would be 3-2.4 = 0.6*10^8m. If we apply length contraction we get 0.6*10^8*γ = 1*10^8m, but this does not agree with the previous calculation of 1.8 *10^8m separation.

Can someone help me understand what I'm doing wrong?

(Apologies if this has terrible formatting, I'm writing from a mobile device!)