GMAT
题目
One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them four hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?
解析
### 解答：
设男人、女人、女孩每小时的工作量分别为\( m \)、\( w \)、\( g \)。
根据题意可得方程：
1. \( m + w = \frac{1}{2} \)
2. \( w + 2g = \frac{1}{2} \)
3. \( m + g = \frac{1}{4} \)
要求1个女人、1个男人和1个女孩一起砌墙所需的时间\( n \)，需先求三人每小时的总工作量，再计算\( n = \frac{1}{m + w + g} \)。
由方程(1)和(2)可得：\( m = 2g \)；
结合方程(3)，可解得：\( g = \frac{1}{12} \)，\( m = \frac{1}{6} \)，\( w = \frac{1}{3} \)。
因此，三人每小时总工作量为\( m + w + g = \frac{7}{12} \)，所需时间\( n = \frac{1}{\frac{7}{12}} = \frac{12}{7} \)。
答案：D
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