This is based on the conservation of momentum - The total momentum in a closed system remains constant unless an external force acts upon it.
We know the momentum of your bumper car before the collision is 370x2=740 kgm/s. Since your car stops after the collision, all of the momentum must be transferred to the other car.
So we can substitute in the known values:
p=mv
740 = 470*v
v=740/470 = 1.57m/s to 3sf
