Broken more than a few pencils on this one. Please help:

A massless spring of spring constant 20 N/m is placed between two carts. Cart 1 has a mass M1 = 5 kg and Cart 2 has a mass M2 = 2 kg. The carts are pushed toward one another until the spring is compressed a distance 1.6 m. The carts are then released and the spring pushes them apart. After the carts are free of the spring, what are their speeds?

Thanks in advance. I'm getting no traction (heh) or movement (hehe) in the right direction on this one. Almost done.

Question

Broken more than a few pencils on this one. Please help:

A massless spring of spring constant 20 N/m is placed between two carts. Cart 1 has a mass M1 = 5 kg and Cart 2 has a mass M2 = 2 kg. The carts are pushed toward one another until the spring is compressed a distance 1.6 m. The carts are then released and the spring pushes them apart. After the carts are free of the spring, what are their speeds?

Thanks in advance. I'm getting no traction (heh) or movement (hehe) in the right direction on this one. Almost done.

anonymous · Answer

So far, I am sure of the following: The system is closed - all energy is conserved. Also the Potential energy of the spring is as follows:
U=k(x^2)/2 = 20(1.6*1.6)/2=51.2/2=25.6(kg m^2/s^2)

anonymous · Answer

m1v1=m2v2, therefore 5kg*v1 = 2kg*v2

anonymous · Answer

I don't know if you have solved this problem yet.  
I was considering the following, using conservation of energy:

$$U _{spring}=KE _{mass}$$
The displacement of each mass would be 1/2 of the compressed distance, so each would move 0.8m