AMC 8 2006 Problem 16
AMC8 2006 年第 16 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. Before Chandra and Bob start reading, Alice says she would like to team read with them. If they divide the book into three sections so that each reads for the same length of time, how many seconds will each have to read?
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。在 Chandra 和 Bob 开始阅读前，Alice 说她想加入和他俩一起团队阅读。若他们把书分成 3 部分，使得每人阅读时间都相同，那么每人阅读时间是多少秒？
- A.6400
- B.6600
- C.6800
- D.7000
- E.7200
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
The amount of pages Bob, Chandra, and Alice will read is in the ratio 4:6:9. Therefore, Bob, Chandra, and Alice read 160, 240, and 360 pages respectively. They would also be reading for the same amount of time because the ratio of the pages read was based on the time it takes each of them to read a page. Therefore, the amount of seconds each person reads is simply .
We can solve this using equations. Let Bob read pages and Chandra read pages. Then Alice would read 760-x-y pages. Then we can set up the equations using the time it takes them to read a page: 45x=30y=20(760-x-y). Since we only have two variables, we only need two equations. Let's use 45x=30y and 45x=20(760-x-y). We can simplify 45x=30y down to 3x=2y and 45x=20(760-x-y) down to 9x=4(760-x-y). We can then solve the equations accordingly: 9x=3040-4x-4y 13x=3040-4y From the equation 3x=2y, we know that 4y=6x. 13x=3040-6x 19x=3040 x=160 Now that we know , we can multiply it by 45 (Bob's speed) to get the answer: 160×45 = 7200
继续练习