I'm starting to study the special theory of relativity, so the concepts and the 'methods' to solve problems are still not very clear in my mind. The question is basically:
A person is running towards a tunnel (which has length $L$) with velocity $v$, at the moment she's about to enter, a photon is emitted on the other side of the tunnel. when the photon and the person encounter each other, the length traveled by the person was $f$. Find $f$ in two different ways: working on the reference frame of the person and working in the reference frame of the tunnel.
I know I have two simultaneous events (in the reference frame of the tunnel): the entry of the person on the tunnel and the photon emission, right? but I have a third one: it occurs after some time interval in the same point in space (where the person encounter with the photon), so here's all I could do:
working in the reference frame of the tunnel: the simultaneous event ((L,0)) as viewed by the tunnel occurs in $x=\gamma(L + vt')={\gamma}L$. The encounter of the person with the photon ((L-f, t')) as viewed by the tunnel in $x=\gamma(L-f + vt')$ (or should it be ct?). I'm really confused of how to start this. I know the right thing to do is using Lorentz transformations, but nothing clear comes to my mind.