2014 AMC 12B Problem 3

Attempt Problem 3 of the 2014 AMC 12B 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 2014 AMC 12B solutions, or check the answer key.

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

Randy drove the first third of his trip on a gravel road, the next

20

miles on pavement, and the remaining one-fifth on a dirt road. In miles, how long was Randy’s trip?

30

\dfrac{400}{11}

\dfrac{75}{2}

40

\dfrac{300}{7}

The paved stretch is the fraction of the trip not on gravel or dirt

That paved fraction

1-\tfrac13-\tfrac15

equals

20

miles

The fraction of the trip on pavement is

1 - \tfrac13 - \tfrac15 = \tfrac{7}{15}.

Since this equals

20

miles, the whole trip is

20 \div \tfrac{7}{15} = \tfrac{300}{7}

miles.

Thus, the correct answer is E.

Problem 3 in other years