13.410 Along the sides of a right angle, towards the vertex, two spheres with radii of 2 and 3 cm are moving, with the centers of these spheres moving along the sides of the angle at unequal but constant speeds. At a certain moment, the center of the smaller sphere is 6 cm from the vertex, and the center of the larger sphere is 16 cm away. After 1 second, the distance between the centers became 13 cm, and after another 2 seconds, the spheres collided without reaching the vertex. Find the speeds of the spheres.