1972 AMC 12 第 15 题

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

设墙中砖的总数为

N

Let

N

be the number of bricks in the wall

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

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.

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