Solders and dog

There is a column of soldiers fifty feet long. At the end of the line
there is a dog. The dog begins to run forward at exactly the same time
that the column begins to march forward. The dog runs to the head of the
column and then, without loosing any time he turns back and and runs
towards the rear of the column. He gets to the end of the line of
soldiers just as the column advances 50 feet. What is the distance
covered by the dog? (Assume that both the dog and the soldiers travel at
constant speeds.)

Answer:

when the dog ran on one way, the solders had marced 25 feet, and dog travelled 75 feet,
and by the time it could com back, the solders had marched another 25 feet, and dog travelled 25 feet.
so in total 100 feet