Question

一名承包商估计，两名砌砖工中一人砌完某面墙需要 $9$ 小时，另一人需要 $10$ 小时。但他根据经验知道，两人一起工作时，合计效率会每小时减少 $10$ 块砖。由于赶时间，他让两人共同施工，发现恰好 $5$ 小时砌完。这面墙共有多少块砖：

A contractor estimated that one of his two bricklayers would take $9$ hours to build a certain wall and the other $10$ hours. However, he knew from experience that when they worked together, their combined output fell by $10$ bricks per hour. Being in a hurry, he put both men on the job and found that it took exactly $5$ hours to build the wall. The number of bricks in the wall was:

$500$

$550$

$900$

$950$

$960$

答案：C

知识点：速率一次方程

难度评级：1790

小提示：

设墙中砖的总数为 $N$

Let $N$ be the number of bricks in the wall

大提示：

两人的实际合计每小时效率为 $\frac{N}{9}+\frac{N}{10}-10$

Their actual combined hourly rate is $\frac{N}{9}+\frac{N}{10}-10$

解答：

若墙中有 $N$ 块砖，两人的单独效率分别为 $\frac{N}{9}$ 和 $\frac{N}{10}$ 。因此 $5\left(\frac N9+\frac N{10}-10\right)=N\text{。}$ 两边乘以 $18$ 并化简，得 $19N-900=18N$ ，故 $N=900$ 。

因此，正确答案是 C。

If the wall contains $N$ bricks, the individual rates are $\frac{N}{9}$ and $\frac{N}{10}.$ Thus $5\left(\frac N9+\frac N{10}-10\right)=N.$ Multiplying by $18$ and simplifying gives $19N-900=18N,$ hence $N=900.$

Therefore, the correct answer is C.

1972 AMC 12 第 15 题

答案：C

难度评级：1790

小提示：

大提示：

解答：

其他年份的第 15 题