How many spare tyres are needed?

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I am about to start a $27,000$ km trip. I check the specifications of tyres to use to find that each is good for only $18,000$ km. What is the fewest number of spare tyres I need to take so I can make it home without having to buy any more?

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Hint: If using a tyre for one km is a unit we will call a tyre-km, how many tyre-km in your trip?

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Hint: What happens right after the first $18,000$ kms?