AMC 8 2006 Problem 15
AMC8 2006 年第 15 题
工程问题★★★☆☆
A Novel Assignment The students in Mrs. Reed's English class are reading the same 760-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds. 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?
Reed 老师英语课上的学生都在读同一本 760 页的小说。班上的三位朋友 Alice、Bob 和 Chandra 读书速度不同：Alice 每页用 20 秒，Bob 每页用 45 秒，Chandra 每页用 30 秒。Chandra 和 Bob 各自都有这本书，他们决定通过”团队阅读”这本小说来节省时间。在这种方案下，Chandra 会从第一页读到某一页，Bob 会从下一页一直读到第 760 页，把书读完。当他们都完成各自的任务，他们会告诉对方自己所读的内容。那么为了使得 Chandra 和 Bob 阅读的时间相同，Chandra 所读的最后一页是第几页？
- A.425
- B.444
- C.456
- D.484
- E.506
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
Same as the previous problem, we only use the information we need. Note that it's not just Chandra reads half of it and Bob reads the rest since they have different reading rates. In this case, we set up an equation and solve. Let be the number of pages that Chandra reads. 30x = 45(760-x) Distribute the 45: 30x = 45(760) - 45x. Add to both sides 75x = 45(760) Divide both sides by 15 to make it easier to solve 5x = 3(760) Divide both sides by 5: x = 3(152) = 456. Chandra and Bob read at a rate of seconds per page, respectively. Simplifying that gets us Bob reads 2 pages for every 3 pages that Chandra reads. Therefore Chandra should read = of the book.
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