AMC8 2006

AMC8 2006 · Q16

AMC8 2006 · Q16. It mainly tests Ratios & proportions, Rates (speed).

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?

在钱德拉和鲍勃开始阅读之前，爱丽丝说她想和他们一起组队阅读。如果他们将书分成三部分，使得每个人阅读的时间相同，那么每个人需要阅读多少秒？

(A) 6400 6400

(B) 6600 6600

(D) 7000 7000

(E) 7200 7200

Answer

Correct choice: (E)

正确答案：（E）

Solution

(E) The least common multiple of 20, 45 and 30 is $2^2 \cdot 3^2 \cdot 5 = 180$. Using the LCM, in 180 seconds Alice reads $\frac{180}{20} = 9$ pages, Chandra reads $\frac{180}{30} = 6$ pages and Bob reads $\frac{180}{45} = 4$ pages. Together they read a total of 19 pages in 180 seconds. The total number of seconds each reads is $\frac{760}{19} \cdot 180 = 7200$.

（E）20、45 和 30 的最小公倍数是 $2^2 \cdot 3^2 \cdot 5 = 180$。利用最小公倍数，在 180 秒内，Alice 读了 $\frac{180}{20} = 9$ 页，Chandra 读了 $\frac{180}{30} = 6$ 页，Bob 读了 $\frac{180}{45} = 4$ 页。他们一共在 180 秒内读了 19 页。则每个人读书的总秒数为 $\frac{760}{19} \cdot 180 = 7200$。

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