When a cylinder rolls without slipping along a horizontal plane, the line with which it makes contact with the plane at any given moment is at rest and the cylinder itself is rotating about this line. In the case given, then, the line of contact with the board is clearly moving forward at a speed twice as great as that of the axis of the drum. Therefore, when a man pushes the board and moves forward a distance equal to the length of the board, the drum will move forward a distance equal to half the length of the board. Thus the man must move a distance of 2l in order to reach the drum.
This can easily be verified with a round pencil and a ruler.