Hello there. To solve this question, we'll have to remember some properties about the triangular inequality.
Given the following triangle in which the buses A, B and C are its vertex:
We know that Bus C is 8 miles away from bus B and bus C is 23 miles away from bus A.
We want to determine the possible distances between the buses A and B.
For this, remember the triangular inequality:
For any three sides of a triangle, say x, y and z, the biggest side z has to satisfy
So we're able to find an inequality that gives us the possible sides of the triangle, and, hence, the distances between the buses.
Plugging x = 8 and y = 23, we get
Also, z has to be greater than or equal to 23, since it is the biggest side, therefore
So the possible values we can choose from the options are between 23 and 31.
These are the answers in this case: 23, 25, 27 and 30