Short answer: about five seconds.

Long answer: on Wikipedia, I found the acceleration to 100, 200 and 300 km/h, which I plotted in a graph with Excel (red is the 80mph car, blue is the F1 car). I added a trendline, which returns a third degree polynomial. This can be integrated, which gives the distance travelled and can be plotted in a graph along with the distance travelled by the car. The intersection between the two graphs is the point at which the F1 car overtakes the car: 4.7 seconds, with 170 metres travelled.

http://www.flickr.com/photos/77889303@N07/9036324580/

I’d say it also depends on driver: for instance, Mark Webber will overtake the car after 6 seconds :P