2014 AMC 12B 第 3 题

Question

Randy 旅程的前三分之一在碎石路上行驶，接着在铺装路上行驶

20

英里，剩下的五分之一在土路上行驶。Randy 的旅程总长多少英里？

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}

铺装路部分是全程中不在碎石路或土路上的那一部分。

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

铺装路所占比例

1-\tfrac13-\tfrac15

对应

20

英里。

That paved fraction

1-\tfrac13-\tfrac15

equals

20

miles

铺装路占全程的比例为

1 - \tfrac13 - \tfrac15 = \tfrac{7}{15}\text{。}

因为这部分等于

20

英里，所以全程为

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

英里。

所以正确答案是 E。

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.

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