Full Speed Ahead!

Have you ever driven a bumper car? Probably you have. Those cars race around in zigzag. The cars are protected with a broad and thick rubber ring so that collisions aren't a problem. If we stick to all safety regulations, collisions are no problem for us. Now, what happens if two bumper cars, which have the same speed, collide frontally?
(We'll make it simpler. Let's assume the two people driving the cars have the same bodyweight.)
The picture shows you the situation in a model experiment. The spring ring at the front is very elastic, just like the rubber ring on bumper cars.

First, think closely if you have ever observed a similar situation already.
What do you think? What will happen?