Final answer:
The problem statement seems to contain an error as solving using the Segment Addition Postulate results in w = 6, which is not listed among the answer choices. Subsequently, the length of RS is found to be 13 when using the correct value of w.
Step-by-step explanation:
The question involves using the Segment Addition Postulate to solve for the variable w, and then finding the length of segment RS. Given is that points R, S, and T are collinear with S between R and T, and we have RS = 2w + 1, ST = w - 1, and RT = 18. By the Segment Addition Postulate, RS + ST = RT. Plugging in the given expressions, we have (2w + 1) + (w - 1) = 18.
Simplifying, we get 3w = 18, and solving for w gives us w = 6, which is not an option in the provided multiple-choice answers. This indicates a potential error in the problem statement. However, continuing with the correct value of w, we substitute w back into the expression for RS: RS = 2(6) + 1, which results in RS being 13. Since none of the provided options match this solution, there might be a typo in the original question or the provided options.