AMC12 2014 B

AMC12 2014 B · Q3

AMC12 2014 B · Q3. It mainly tests Fractions, Ratios & proportions.

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?

Randy 的行程前三分之一在碎石路上，接下来 20 英里在铺装路上，剩余五分之一在土路上。Randy 的总行程多长（英里）？

(A) 30 30

(B) \frac{400}{11} \frac{400}{11}

(D) 40 40

(E) \frac{300}{7} \frac{300}{7}

Answer

Correct choice: (E)

正确答案：（E）

Solution

The fraction of Randy’s trip driven on pavement was $1 - \frac{1}{3} - \frac{1}{5} = \frac{7}{15}$. Therefore the entire trip was $20 \div \frac{7}{15} = 20 \cdot \frac{15}{7} = \frac{300}{7}$ miles.

Randy 在铺装路上行驶的比例是 $1 - \frac{1}{3} - \frac{1}{5} = \frac{7}{15}$。因此整个行程是 $20 \div \frac{7}{15} = 20 \cdot \frac{15}{7} = \frac{300}{7}$ 英里。

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