1961 AMC 12 Problem 2

Attempt Problem 2 of the 1961 AMC 12 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 1961 AMC 12 solutions, or check the answer key.

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

2.

An automobile travels a6\frac{a}{6} feet in rr seconds. If this rate is maintained for 33 minutes, how many yards does it travel in the 33 minutes?
a1080r\dfrac{a}{1080r}
30ra\dfrac{30r}{a}
30ar\dfrac{30a}{r}
10ra\dfrac{10r}{a}
10ar\dfrac{10a}{r}
Answer: E
Concepts:distance rate and timeunit conversion
Small hint:
Convert 33 minutes to seconds
Big hint:
After finding the distance in feet, divide by 33 to convert to yards
Solution:
The speed is a6r\frac{a}{6r} feet per second. In 180180 seconds the automobile travels 180⋅a6r=30ar 180\cdot\frac{a}{6r}=\frac{30a}{r} feet, or 10ar\frac{10a}{r} yards.
Thus, the correct answer is E.
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