AMC12 2008 B

AMC12 2008 B · Q10

AMC12 2008 B · Q10. It mainly tests Linear equations, 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?

砌砖工 Brenda 独自砌一个烟囱需要 $9$ 小时，砌砖工 Brandon 独自砌需要 $10$ 小时。他们一起工作时话很多，导致他们的合计产量每小时减少 $10$ 块砖。他们一起用 $5$ 小时砌完了烟囱。烟囱共有多少块砖？

(A) 500 500

(B) 900 900

(D) 1000 1000

(E) 1900 1900

Answer

Correct choice: (B)

正确答案：（B）

Solution

Let $h$ be the number of bricks in the chimney. Without talking, Brenda and Brandon lay $\frac{h}{9}$ and $\frac{h}{10}$ bricks per hour respectively, so together they lay $\frac{h}{9}+\frac{h}{10}-10$ per hour together. Since they finish the chimney in $5$ hours, $h=5\left( \frac{h}{9}+\frac{h}{10}-10 \right)$. Thus, $h=900 \Rightarrow B$.

设烟囱共有 $h$ 块砖。如果不聊天，Brenda 和 Brandon 的砌砖速度分别为每小时 $\frac{h}{9}$ 块和 $\frac{h}{10}$ 块，因此他们一起每小时砌 $\frac{h}{9}+\frac{h}{10}-10$ 块。由于他们用 $5$ 小时完成烟囱，有 $h=5\left( \frac{h}{9}+\frac{h}{10}-10 \right)$。因此 $h=900 \Rightarrow B$。

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