State a rule that describes how to predict the relative velocities of the two carts after the explosion.

-answer

If this explosion is occurring in a closed environment this 'rule' would be:

The conservation of momentum.

Explanation:

In a close system which means the experiment is isolated from the surrounding environment and therefore not allowed to interact with its external space will have the same amount of momentum at the end of the experiment as the beginning by the equation of p=mv, p is momentum, m is mass and v is velocity.

conservation of mass

mass before something happens = mass afterwards