The race clinic is the same Saturday as Sprint Series(a monthly karting race series). It lasts 10 months. The Sprint Series will be the best series to engage beginning drivers into karting. If you are looking to get more serious you may want to check out an LAKC or TriC event at CalSpeed. There are a few different classes(different karting...not school) in those events. Mostly an arrive and drive full sprint series($95) day with race clinic ($135)will cost around 220+/-. They have race gear available for you. Helmets also. Most public races last 10 mins on track and that's about 10 laps, give or take. The track is 7/10th of mile +/- depending on the layout for that particular month. Come out and have fun.
Check out their web page for Cal Speed Karting. They have an event calander. Pick a day that isn't a race or race practice. They have lots of options for open practice to rent karts. Prices are good. If you want to kick it up reach out to MRC for shifters.
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