Collision

The equation of relative motion of the two body system is :

$\dfrac{d\vec v_{rel}}{dt}=\dfrac{\vec {F_2}}{m_2}-\dfrac {\vec {F_1}}{m_1}-\dfrac {\vec F_{12}}{\mu}$ . Here $\vec {F_1}=40$ N is the force applied to the body of mass $m_1=40$ kg., $\vec {F_2}=20$ N is the force applied to the body of mass $m_2=10$ kg., $\vec F_{12}$ is the force exerted by the spring on the bodies, equal to $56\vec x_{rel}$ N, $\vec x_{rel}$ is the displacement of the first body relative to the second, $\vec v_{rel}$ is their relative velocity, and $\mu=\dfrac{m_1m_2}{m_1+m_2}=8$ kg. is the reduced mass of the system. Solving this equation using the initial condition we get

$v_{rel}^2=1+6x_{rel}-7x_{rel}^2$ .

When the spring compression is maximum, $v_{rel}=0$ . This will happen when $7x_{rel}^2-6x_{rel}-1=0\implies x_{rel}=\boxed 1$ m.