Locations of Jack's home, school, and gym form an obtuse triangle on the map.

Question

Let A be the difference between the distance from Jack's home to the school and the distance from the home to the gym. Let B be the distance from the school to the gym.

Is A greater than B, B greater than A, A equal to B, or can't be determined?

Answer 1

can't be determined. If the sides of a triangle are a,b,c from least to greatest, you must have
b-a < c < b+a
since you have not specified the obtuse angle in your diagram, there is no way to determine which side is the longest.

I get the feeling you want A < B, and that may be so, bu it cannot be determined from what you said.

Answer 2

Why would it not be A greater than B? By the Triangle Inequality a + b > c for any triangle to exist. A picks any two sides which must be greater than the distance of a single side.