Suppose B goes north for X kilometers, because the speed ratio of A and B is 3: 1.

So the total distance of A is eastward plus the tangent length ***3x km.

Assuming that A walks y kilometers to the east, then A walks (3x-y) kilometers in the tangential direction;

For the triangle formed by the tangent and the east and north directions, we can know it by the proportional relationship of similar right-angled triangles.

Village radius /B distance traveled = distance traveled eastward/distance traveled tangent.

That is, R/x=y/3x-y, so y=9x/(x+3).

According to the right angle △ Pythagorean theorem, it is concluded that x square +y square =(3x-y) square.

So the square of x +[9x/(x+3)] is the square of (3x) [1-3/(x+3)].

That is 4x squared -3x-45=0.

So x= 15/4 or -3 (truncation)

So A and B meet at a distance of 15/4 km from the center of true north.