solution:

Because it is an elastic collision, both kinetic energy and momentum are conserved. We can make two equations, one for the conservation of KE, and one for the conservation of momentum. There are two unknowns in each equation ( of each block) and we will solve for one and plug it into the other equation.

I will now solve for in eqn (4) and plug it into eqn (3) and solve for

Now use the Quadratic Equation to solve for :

It is clear that it can't be 4m/s because that was its original velocity.

Another way to solve the problem in a much easier fashion is to know that the relative velocities before and after the collision must be equal. Use the relation and the conservation of momentum, and you will end up with the same answer without nearly as much algebra.