A 15 kg object moving to the right a 22.5 m/s makes an elastic head on collision with a 30 kg object moving to the left at 18 m/s. After the collision the smaller object 15 kg object moves to the left at 31.5 m/s. What is the velocity of the 30 kg marble?
9m/s to the right
In an elastic collision, the differences in velocities before and after the collision is the same (to conserve mechanical energy). In your case the difference is 40.5m/s, so if one is 31.5m/s to the left, the other must be 9m/s to the right.