Final answer:
To find BM when M is the midpoint of AB, equate the expressions for AM and MB, solve for x, and substitute back to get BM = 23 meters.
Step-by-step explanation:
The question requires solving for BM given that point M is the midpoint of AB and the expressions for AM and MB are 4x - 25 and 3x - 13 respectively. Being the midpoint means that AM is equal to MB. Thus, we set the expressions equal to each other to solve for x: 4x - 25 = 3x - 13. Solving for x gives us x = 12. Substituting x back into the expression for BM gives us BM = 3(12) - 13, which simplifies to BM = 36 - 13, hence finding BM = 23 meters. This calculation finds the length of segment BM given the midpoint M.