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Let us suppose our old friend the railway carriage to be

travelling along the rails with a constant velocity v, and that a

man traverses the length of the carriage in the direction of

travel with a velocity w. How quickly or, in other words, with

what velocity W does the man advance relative to the embankment

during the process? The only possible answer seems to result from

the following consideration: If the man were to stand still for a

second, he would advance relative to the embankment through a

distance v equal numerically to the velocity of the carriage. As

a consequence of his walking, however, he traverses an additional

distance w relative to the carriage, and hence also relative to

the embankment, in this second, the distance w being numerically

equal to the velocity with which he is walking. Thus in total he

covers the distance W = v + w relative to the embankment in the

second considered.