The purpose of speed limits is to keep driving speed low enough for drivers to be able to pay attention to relevant information and timely execute maneuvers so that the car can be driven in a safe way and stopped in time. If a driver violates a speed limit or drives too fast she or he will not be able to stop as quickly as from a slower speed. We asked participants to imagine that they themselves had driven a car outside a school at a speed of 30 km/h when a child suddenly had rushed into the street. From this speed it was possible to stop the car just in front of the child after braking as quickly and forcefully as possible. We then asked the participants to imagine that they drove the same street at a higher speed of 50 km/h and the child appeared at the same place as before. At what speed would the car hit the child after braking in the same way as before? This kind of problems were presented in three studies and the results showed that the judged speeds of collision were always underestimated in different hypothetical driving context scenarios by judges differing in numerical skills. This indicates an overly optimistic view on the possibilities to reduce speed quickly if the driving speed is too fast, which is an important component of attitudes towards speed limits, their legitimacy and recommended driving speeds. Further implications of the results were discussed last.