AMC10 2008 B

AMC10 2008 B · Q18

AMC10 2008 B · Q18. It mainly tests Work problems.

Bricklayer Brenda would take 9 hours to build a chimney alone, and bricklayer Brandon would take 10 hours to build it alone. When they work together, they talk a lot, and their combined output is decreased by 10 bricks per hour. Working together, they build the chimney in 5 hours. How many bricks are in the chimney?

砖瓦工 Brenda 独自砌烟囱需要 9 小时，Brandon 独自需要 10 小时。他们一起工作时聊天很多，每小时总产量减少 10 块砖。他们一起用 5 小时砌完了烟囱。烟囱中共有几块砖？

(A) 500 500

(B) 900 900

(D) 1000 1000

(E) 1900 1900

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Let $n$ be the number of bricks in the chimney. Then the number of bricks per hour Brenda and Brandon can lay working alone is $\frac{n}{9}$ and $\frac{n}{10}$, respectively. Working together they can lay $\left(\frac{n}{9}+\frac{n}{10}-10\right)$ bricks in an hour, or $5\left(\frac{n}{9}+\frac{n}{10}-10\right)$ bricks in 5 hours to complete the chimney. Thus $5\left(\frac{n}{9}+\frac{n}{10}-10\right)=n,$ and the number of bricks in the chimney is $n=900$.

答案（B）：设 $n$ 为烟囱中的砖块数量。则 Brenda 和 Brandon 单独工作时每小时分别能砌 $\frac{n}{9}$ 和 $\frac{n}{10}$ 块砖。两人一起工作时，每小时能砌 $\left(\frac{n}{9}+\frac{n}{10}-10\right)$ 块砖，因此在 5 小时内可砌 $5\left(\frac{n}{9}+\frac{n}{10}-10\right)$ 块砖来完成烟囱。于是 $5\left(\frac{n}{9}+\frac{n}{10}-10\right)=n,$ 所以烟囱中的砖块数量为 $n=900$。

Topics

AR.008 Work problems