Discussion and hints:

It is recommended that you work with the system made up of A and B together. With such a system, you can avoid dealing with the internal spring force when using the linear impulse-momentum equation.

Step 1: FBDs
Draw an FBD of A+B.
Step 2: Kinetics (linear impulse/momentum)
Look for forces acting in the direction of travel for your FBD. Is linear momentum conserved in that direction? Also, note that you are asked to find the velocity of both A and B (two unknowns); however, the linear impulse-momentum equation is only a single equation. Where do you go for the second equation? Think about the work-energy equation.
Step 3: Kinematics
What are the kinematics of A and B corresponding to maximum compression of the spring?
Step 4: Solve

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Any questions?