AMC 8 2006 Problem 14

AMC8 2006 年第 14 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. If Bob and Chandra both read the whole book, Bob will spend how many more seconds reading than Chandra?
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。如果 Bob 和 Chandra 都读完整本书,Bob 比 Chandra 多用多少秒?
  1. A.7,600
  2. B.11,400
  3. C.12,500
  4. D.15,200
  5. E.22,800

正确答案 · Correct Answer

B

解析 · Solution

Solution 1

The information is the same for Problems 14,15, and 16. Therefore, we shall only use the information we need. All we need for this problem is that there's 760 pages, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds. A lot of people will find how long it takes Bob to read the book, how long it takes Chandra to read the book, and then find the seconds. However, if we just set up the expression, we can find an easier way. 760⋅45−760⋅30=760(45−30)=760(15)=11,400760\cdot45 - 760\cdot30 = 760(45-30) = 760(15) = 11,400

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