Answer:
14" + 3/4" (but already there are two ribbons with that lenght, so probably the is answer is not adding no one more)
Explanation:
If we call:
U : the longest ribbon (wich we don't know)
L : the lowest ribbon (wich one could be know, see the plot)
The condition is:
U - L = 1"+1/8" ----> U = L + 1" + 1/8" ---(A)
Calculating L:
Between 14 and 15 there are 8 spaces, then if we call to the long of that tiny space 'p', then:
8*p = 15"- 14" ---> p = (15"-14")/8 ---> p = 1"/8
In the plot, we see what 'L' is three spaces under 14", then:
L= 14" - 3*p = 14" - 3*(1"/8) = 14" - 3/8"
Replacing this result in the (A) expresion:
U = (14" - 3/8") + 1" + 1/8" = 14"+1" -3/8" + 1/8" = 14" + 6/8" = 14" + 1/4"
Then: U = 14" + 3/4"