Atrain with proper length l has clocks at the front and back. a photon is fired from the front to the back. working in the train frame, we can easily say that if the photon leaves the front of the train when a clock there reads zero, then it arrives at the back when a clock there reads l/c. now consider this setup in the ground frame, where the train travels by at speed v. rederive the above frame-independent result (namely, if the photon leaves the front of the train when a clock there reads zero, then it arrives at the back when a clock there reads l/c) by working only in the ground frame.