Question 1192513
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Although it is not disclosed in the post, from the context I can guess that

AC and CB are the legs of the right-angled triangle ABC, while AB is its hypotenuse.



Then, using the Pythagorean theorem, I can find the length of AB

   AB {{{sqrt(8^2+15^2)}}} = {{{sqrt(64+225)}}} = {{{sqrt(289)}}} = 17 miles.



Next, the problem asks how much longer is the path AC + CB than AB.


To find it, subtract  17 from 8+15:  


            (8+15) - 17 = 23 - 17 = 6.


<U>ANSWER</U>.  The path AC + CB is 6 miles longer than AB.
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Solved (with clear explanations).