Math CentralQuandaries & Queries


Question from rachel, a student:

two men were about to start on an 18,000 mile automobile trip. The tires on their car were each good for 12,000 miles but not a foot more. how many spares will they need to go 18,000 miles

Hi Rachel.

Assuming they have a normal four-tired vehicle, they have a total of 4 x 18,000 = 72,000 miles of wear to put on some tires. If each tire is good for 12,000 miles, then they need 72,000 / 12,000 = 6 tires in total, but they need to plan carefully to make sure they rotate them at the right time, or they'll be stuck!

Here's one of many ways they could do it using tires A. B. C. D. E. F:

leg of trip A B C D E F
0-2000 X   X X X  
2-4000 X X X X    
4-6000 X X   X X  
6-8000 X X X     X
8-10000 X X   X   X
10-12000 X X     X X
12-14000   X X   X X
14-16000     X X X X
16-18000     X X X X

Stephen La Rocque.

PS: With the price of gas these days, I'd be more concerned about the fuel price of this trip than the tires! :)

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