How Does Spring Compression Affect Mass Velocity on a Frictionless Table?

[pdubb]

A massless spring is between a 1-kilogram mass and a 3-kilogram mass, but it is not attached to either mass. Both masses are on a horizontal frictionless table. In an experiment, the 1-kilogram mass is held in place, and the spring is compressed by pushing on the 3-kilogram mass. The 3-kilogram mass is then released and moves off with a speed of 10 meters per second.

(a) Determine the minimum work needed to compress the spring in this experiment.
(b) Determine the final velocity of each mass relative to the cable after the masses are released.

I am totally lost on this problem. I mean, I understand what it is asking for, but I don't know which equation to use and what variables to solve for. I know the equation for work is W= 1/2kx^2.
I know that when the spring is compressed with mass of 3 kg, then there's only spring potential energy, when the mass is released with a speed of 10m/s then there's only kinetic energy, but i don't know what to do to solve this problem.

 

[CaptainZappo]

Assuming both masses are released, I believe you should also consider what the 1 kg mass is doing. What does conservation of momentum tell you? Being that kinetic energy is a scalar quantity, how can you relate the movement of these two masses to the minimum input work required?