John T. answered • 03/01/16
Tutor
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You need only 6 new tires at the beginning of the trip. Rotate the two new spares in at 2000 miles. The two tires taken off will have 6000 miles left on them. Then rotate the 6000-mile spares back in at 4000 miles, setting two tires with 4000 miles each off as spares. Repeat this process until the trip is completed. All six tires will be completely used up after 12000 miles with no rubber wasted at the end.
John T.
tutor
Use digits to represent one tire and the miles (x1000) left in the lifetime of that particular tire. Make a table of rotations:
Rotation On The Car Spares
Start 8 8 8 8 8 8
2K miles 6 6 8 8 6 6
4K miles 6 6 6 6 4 4
6K miles 4 4 4 4 4 4
8K miles 2 2 4 4 2 2
10K miles 2 2 2 2 0 0
12K miles 0 0 0 0 0 0
The mathematical way is to figure out how many total tire-miles you need. It is 12,000 miles for the trip times 4 tires so 48,000 tire-miles needed. Divide that number by 8,000 miles of wear per tire, and you get 6.
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03/18/16
Ximena L.
03/01/16