These Tires Don't Last Long

Algebra Level 3

Albert is driving a scooter. He brings a spare tire. A tire can last for 5 kilometers. How many km can Albert travel with these tires?

Assumption : A scooter needs two tires. Albert's scooter already has two tires, so with the spare tire there are three tires. All of them are new when Albert begins his journey. Albert can change his tire configuration at any time.

5 0 15 7.5 10

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2 solutions

Pushpang Singh
Jan 12, 2016

Albert will first move 2.5 kms then he will change one tyre(suppose the back one) with an extra one. Then he will again move 2.5 kms so the front one will be destroyed because it can last for 5 kms only.Then he will change the front tyre with the back one which he took away earlier.After changing he'll move 2.5 kms more and thus his all three tyres will be destroyed . So, the total distance traveled will be 7.5 kms.

I didn't understand the first line?

arifuzzaman arif - 5 years, 5 months ago

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Here A means Albert

After moving 2.5 kms he can change any tyre but to avoid confusion I am mentioning that he took out back one.

Pushpang Singh - 5 years, 5 months ago
Jerry Hill
Jan 17, 2016

We have 3 tires - A, B and C each with a life of 5 kms.

Configuration : A and B

Albert travels 2.5 kms with tires A and B and replaces A (or B, as the case may be) with C. (At this point, A and B will have 2.5 kms remaining and C has 5 kms)

New Configuration : A and C

Albert travels another 2.5 kms with tires A and C and replaces tire A with B. (At this point, B has 2.5 kms left and C has 2.5 kms left)

New Configuration : B and C

Then Albert travels another 2.5 kms with tires B and C.

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