2014 AMC 10B 第 3 题

Question

Randy 旅程的前三分之一是在碎石路上行驶，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}

铺装路部分是减去碎石路和土路比例后剩下的部分。

The paved part is what remains after the gravel and dirt fractions

令全程的

\frac7{15}

等于

20

。

Set

\frac7{15}

of the trip equal to

20

设全程为

t

英里，则

\begin{aligned}t &= \dfrac t5 + 20 + \dfrac t3 \\ t &= 20 + \dfrac {8t}{15} \\ \dfrac 7{15} t &= 20\\ t &= \dfrac{300}7\end{aligned}\text{。}

所以正确答案是 E。

Let the path distance be

t.

Then, we get:

\begin{aligned}t &= \dfrac t5 + 20 + \dfrac t3 \\ t &= 20 + \dfrac {8t}{15} \\ \dfrac 7{15} t &= 20\\ t &= \dfrac{300}7.\end{aligned}

Thus, the correct answer is E .

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