According to Kepler's third law, $T^2 \propto R^3$, where R is the orbital radius from the center of the earth. The orbital radii are $(R_e+r)$ and $(R_e+2r)$. The problem is ambiguous. Assuming r is orbital radius, $T_A^2/T_B^2 = r^3/(2r)^3 = 1/8$. So $T_A/T_B = 1/\sqrt{8} = 1/(2\sqrt{2})$.