Two blocks are connected to an ideal spring of stiffness 200 N/m. At a certain moment, the two blocks are moving in opposite directions with speeds ${\text{4 ms}}^{-1}$ and ${\text{6 ms}}^{-1}$, and the instantaneous elongation of the spring is 10 cm. The rate at which the spring energy $\left(\frac{k{x}^2}{2}\right)$ is increasing (in Joules per second) is 100n. Find n.