Wanted: Calculate and Display Reaction Time/Elapsed Time

I got my son an Auto World Pro Racing Dragstrip for Christmas.
http://www.youtube.com/watch?v=K3SNzDs_NJI  Great fun out of the box with
the starting tree that alerts false starts and  identifies the winner at the
end of the track.  It does this with electric eyes in the track for each
lane that see when a car passes over it.  Like I said, great fun, but we
would like to see
1) the driver's reaction time - the time it takes from the time the light
turns green to the time the car moves across the eye at the start - and
2) the elapsed time - the time the car moves across the eye at the start to
the time the car crosses the finish.
Ideally, this would be displayed for each lane until reset.  Total elapsed
time and MPH are typically displayed in real life...

I believe this can be accomplished using the existing components in the Auto
World kit and an Arduino.  The following instructables could prove useful...


I am open to all... better ideas, off the shelf solutions, delivered
product, or help developing solution.  This is something I think I could do
with step by step instruction but not something I would attempt on my own.
I know just enough to get me in trouble.