Question

If I have a board 31 1/4 " long and want 13 stripes on it how wide will each stripe be

Answer 1

I'm not sure what you need -- but this is how I interpret your problem.

31.25 / 13 = 2.4038461 inches

Answer 2

Of course, if each stripe is that wide, there will be no space between them, so the board will just be solid white.

Now you have to decide how much blank space to allocate between the stripes, and whether the end stripes will reach to the very ends of the board, or whether there will be blank space at the ends.