Hi,
Arduino is not slow, 1800 rpm is only 30 events per second, which means that your Arduino can perform roughly 500,000 operations between revolutions this is several hundred times more than you need.
Its nice to see that you have a motor sports application, its close to my own interest. I don't know that you are taking the best approach.
Have a look at my RC/Kart lap timer, its uses infra red to time laps, you can create infra red beacons for about 2 dollars that you could position on the track for taking split times automatically.
Its small enough to strap to a steering wheel of a kart, but as I have found that I cannot always look at the wheel the most useful feature is a very loud buzzer. One buzz to confirm a lap/split has been captured and two pips if its a new best, it makes a huge difference to my RC driving, I cannot believe how much harder I work on a lap to get those two pips.
I am working on the project right now and plan to finish it within a few days at which point I will write it up in full, in the meantime check out the relevant blog posts here -
Duane B