Final answer:
The length of segment BF is 11 units.
Step-by-step explanation:
Given that point G is the centroid of triangle ABC, we know that the centroid divides each median in a 2:1 ratio. Let's denote the length of segment BG as x. Since point G is the centroid, BG = 6 can be expressed as 2x = 6. Solving for x, we find that x = 3. Therefore, the length of segment BF can be found by subtracting BG from the total length of the median, which is AE + EG. The length of AE is given as 15 and the length of EG can be found as 2/3 of BG. Substituting the known values, we have EG = (2/3)(3) = 2. Therefore, the length of segment BF is AE + EG - BG = 15 + 2 - 6 = 11 units.