I think you have the wrong name for the game
Try looking for RUSH HOUR
Just checked and theres another game called rush hour which is a clone of Traffic.
the Rush Hour thats on my amiga is like you described.
It is 1 or 2 players. Theres an old woman usually in the center that you can take over the road with you or put in front of a car. Theres a can to kick for bonus points.
After a short time a voice says "Rush Hour" and all the cars speed up
