Question

Chandra 和 Bob 各有一本书，他们决定用“团队阅读”来节省时间。按照这种方法，Chandra 从第 $1$ 页读到某一页，Bob 从下一页读到第 $760,$ 页，读完整本书。读完后他们会互相讲述自己读的部分。为了让 Chandra 和 Bob 阅读时间相同，Chandra 应该读到最后哪一页？

Chandra and Bob, who each have a copy of the book, decide that they can save time by "team reading" the novel. In this scheme, Chandra will read from page $1$ to a certain page and Bob will read from the next page through page $760,$ finishing the book. When they are through they will tell each other about the part they read. What is the last page that Chandra should read so that she and Bob spend the same amount of time reading the novel?

$425$

$444$

$456$

$484$

$506$

答案：C

知识点：速率一次方程

难度评级：1380

解答：

设 Chandra 阅读 $x$ 页，那么 Bob 阅读 $760 - x$ 页。

为了让阅读时间相同， $\begin{align*} 30x &= 45(760 - x) \\ 30x &= 45 \cdot 760 - 45x \\ 75x &= 45 \cdot 760 \\ 5x &= 3 \cdot 760 \\ x &= 3 \cdot 152 \\ x &= 456. \end{align*}$

所以正确答案是 C。

Let $x$ be the number of pages that Chandra will read. Then Bob will read $760 - x$ pages.

For them to read for the same amount of time, $\begin{align*} 30x &= 45(760 - x) \\ 30x &= 45 \cdot 760 - 45x \\ 75x &= 45 \cdot 760 \\ 5x &= 3 \cdot 760 \\ x &= 3 \cdot 152 \\ x &= 456. \end{align*}$

Thus, C is the correct answer.

2006 AMC 8 第 15 题

答案：C

难度评级：1380

解答：

其他年份的第 15 题