It's because the conveyor belt goes all the way around.

The conveyor belt length is the distance between the centres twice,

and a semicircle twice.

Hence the distance between the centres is half of "15 feet minus 2 semicircle lengths".

The diameters of the circles is 1 foot, so their radii is 1/2 a foot.

Finish up by calculating the length of the round part of the belt.