Well, you can't have 4/3 of a rope because 3/3 would be one whole. That is an improper fraction. It would be 1 and 1/3. If you divide that in to two, then you get 2/3. Is that the answer you were looking for?
When Sam is 13 his mother will be 39 which is 3 times as old as he is. So Sam's mother will be 3 times as old as Sam will be in 11 years. (Your answer is 11 years.)