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：1530

解答：

设烟囱有 $n$ 块砖。Brenda 单独工作时每小时砌 $\tfrac{n}{9}$ 块，Brandon 每小时砌 $\tfrac{n}{10}$ 块。一起工作时，他们的效率为 $\tfrac{n}{9} + \tfrac{n}{10} - 10$ 。

工作 $5$ 小时完成烟囱，因此展开得 $\tfrac{5n}{9} + \tfrac{5n}{10} - 50 = n$ ，所以 $\tfrac{95n}{90} - n = 50$ ，从而 $\tfrac{5n}{90} = 50$ 。 $5\left(\tfrac{n}{9} + \tfrac{n}{10} - 10\right) = n.$

因此 $n = 900$ 。

因此，正确答案是 B。

Let $n$ be the number of bricks. Alone, Brenda lays $\tfrac{n}{9}$ bricks per hour and Brandon lays $\tfrac{n}{10}.$ Together, their rate is $\tfrac{n}{9} + \tfrac{n}{10} - 10.$

Working for $5$ hours completes the chimney: $5\left(\tfrac{n}{9} + \tfrac{n}{10} - 10\right) = n.$ Expanding, $\tfrac{5n}{9} + \tfrac{5n}{10} - 50 = n,$ so $\tfrac{95n}{90} - n = 50,$ giving $\tfrac{5n}{90} = 50.$

Hence $n = 900.$

Thus, the correct answer is B.

2008 AMC 12B 第 10 题

答案：B

难度评级：1530

解答：

其他年份的第 10 题