βI solved this problem but I do not know if it is correct becasue there is no way to check it: Imagine that we define the rear end of a train 120 m long to long to define the origin X'=0 in the train frame and we define a certain track signal light to define the origin X=0 in the track frame. Imagine that the rear end of of the train passes this sign at t+t'=0 as the train moves in the +X direction at a constant speed of 25 m/s. 12 seconds later, the engineer turns on the train's heasdlight. A) Where does this event occur in the train frame? B) Where does this event occur in the track frame 2. Relevant equations Use Galilean transformation equations for position. β is the contstant velocity. t=t' x'=X- β*t 3. The attempt at a solution Here is my work: 25m/s*12s=300m 300m+120m= 420m Train Frame 420m 420m=X-300m X=720m Track frame 720m Is this correct?