1992 AMC 8 Problem 12

Attempt Problem 12 of the 1992 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1992 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

12.

The five tires of a car (four road tires and a full-sized spare) were rotated so that each tire was used the same number of miles during the first 30,00030{,}000 miles the car traveled. For how many miles was each tire used?
60006000
75007500
24,00024{,}000
30,00030{,}000
37,50037{,}500
Answer: C
Concepts:rate
Small hint:
At any moment 44 of the 55 tires are on the ground, so the total tire-mileage is 4×30,0004 \times 30{,}000
Big hint:
Share that total tire-mileage equally among the 55 tires
Solution:
During the 30,00030{,}000 miles, 44 tires are always in use, so the total tire-mileage is 4×30,000=120,0004 \times 30{,}000 = 120{,}000 tire-miles.
Split equally among 55 tires, each tire is used 120,0005=24,000\dfrac{120{,}000}{5} = 24{,}000 miles.
Thus, the correct answer is C .
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