A square with side length $P$ is inscribed in a right triangle with legs of length 8 and 15 so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length $Q$ is inscribed in another right triangle with legs of length 8 and 15 so that one side of the square lies on the hypotenuse of the triangle. What is $\frac{Q}{P}$?