题目
If 3 men or 6 boys can do a piece of work in 10 days, working 7 hours a day; how many days will it take to complete a piece of work twice as large with 6 men and 2 boys working together for 8 hours a day?
解析
已知关系:
3个男人 = 6个男孩(即\( M = 2B \))
3个男人或6个男孩完成一项工作,需要10天,每天工作7小时;
总工作量 = \( 3M×10×7 \)
现在让6个男人和2个男孩一起工作,每天工作8小时;
总工作量 = \( (6M+2B)×8×\text{天数} \)
**假设两组完成的工作量相等**:
\( 3M×10×7 = (6M+2B)×8×\text{天数} \)
代入\( B=\frac{M}{2} \),得:\( 3M×10×7 = 7M×8×\text{天数} \)
解得:\( \text{天数} = 3.75 \)
已知实际工作量是原来的两倍,因此所需天数为:\( 3.75×2 = 7.5 \)天