Question

砌砖工 Brenda 单独建一个烟囱需要 $9$ 小时，砌砖工 Brandon 单独建需要 $10$ 小时。他们一起工作时聊天很多，合计产出每小时减少 $10$ 块砖。他们一起工作 $5$ 小时建完烟囱。这个烟囱有多少块砖？

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?

$500$

$900$

$950$

$1000$

$1900$

答案：B

知识点：速率一次方程

难度评级：1370

解答：

设砖块数为 $n$ 。Brenda 每小时砌 $\tfrac{n}{9}$ 块，Brandon 每小时砌 $\tfrac{n}{10}$ 块，所以一起每小时砌 $\tfrac{n}{9}+\tfrac{n}{10}-10$ 块。

他们工作 $5$ 小时共完成 $n$ 块：解得 $\tfrac{5n}{9}+\tfrac{n}{2}-50=n$ ，所以 $n=900$ 。 $5\left(\tfrac{n}{9}+\tfrac{n}{10}-10\right)=n.$

所以正确答案是 B。

Let $n$ be the number of bricks. Brenda lays $\tfrac{n}{9}$ per hour and Brandon $\tfrac{n}{10},$ so together they lay $\tfrac{n}{9}+\tfrac{n}{10}-10$ per hour.

Over $5$ hours this equals $n:$ $5\left(\tfrac{n}{9}+\tfrac{n}{10}-10\right)=n.$ Solving, $\tfrac{5n}{9}+\tfrac{n}{2}-50=n,$ which gives $n=900.$

Thus, the correct answer is B.

2008 AMC 10B 第 18 题

答案：B

难度评级：1370

解答：

其他年份的第 18 题