It totally depends on the situation.
If your kart had a LOT of power, and you constant drifted or did big burnouts,
you could probably wear out a brand new set (of rear tires) down to the cords in 30 seconds.
If you stored your kart outside in the direct sun (hot/cold low-humidity weather) you could dry rot cheap inexpensive tires in just a few months, even without wearing them out by riding your kart.
But If you had super high quality tires,
stored your kart inside in a climate controlled room,
hardly ever rode the kart,
and elevated the kart off the ground so you didn't flat-spot your tires,
and used some type of tire product to replace the oils that evaporate from tires over time:
Your tires might last and be usable for 50 years or more.
Which one of these situations is the closest to your tires?