After t seconds the train headlight has moved
and 
later it will be 
. The taillight however, will be l units behind the head light so event 2 will occur at
. The distance between the two events thus events are separated by,
.
If a frame is moving at speed V then, during time
it will move a distance of V. This distance must exactly be equal to the separation of distance between the two events. Thus, the velocity of the frame should simply be,
