Answer: Their speed is 7.5 km per hour.
Let the speed be x km/hr. In 2 hours each walks 2x km. East and North are perpendicular, so the distance between them is the hypotenuse of a right-angled triangle with both sides 2x:
\[(2x)^2 + (2x)^2 = (15\sqrt{2})^2\] \[8x^2 = 450\] \[x^2 = 56.25,\quad x = 7.5\]