AMC8 2006

AMC8 2006 · Q15

AMC8 2006 · Q15. It mainly tests Linear equations, Rates (speed).

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?

Chandra 和 Bob 各有一本相同的书，他们决定通过“团队阅读”来节省时间。在这种方案中，Chandra 从第1页读到某一页，Bob 从下一页读到第760页，完成整书。完成后他们互相讲述自己读的部分。为了让他们阅读小说所花时间相同，Chandra 应该读到最后一页是第几页？

(A) 425 425

(B) 444 444

(D) 484 484

(E) 506 506

Answer

Correct choice: (C)

正确答案：（C）

Solution

(C) The ratio of time it takes Bob to read a page to the time it takes Chandra to read a page is $45\!:\!30$ or $3\!:\!2$, so Bob should read $\frac{2}{3}$ of the number of pages that Chandra reads. Divide the book into $5$ parts, each with $\frac{760}{5}=152$ pages. Chandra will read the first $3\cdot152=456$ pages, while Bob reads the last $2\cdot152=304$ pages.

（C）鲍勃读一页所需时间与钱德拉读一页所需时间之比为 $45\!:\!30$，即 $3\!:\!2$，因此鲍勃应读钱德拉阅读页数的 $\frac{2}{3}$。把全书分成 $5$ 份，每份有 $\frac{760}{5}=152$ 页。钱德拉读前 $3\cdot152=456$ 页，而鲍勃读后 $2\cdot152=304$ 页。

Topics