题目
Three hoses work to fill a tub at at different rate. Hose A and B, working together, can fill the tub in 6/5 of an hour. Hoses A and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub?
解析
将给定的时间转换为效率,你就可以将它们相加。
A和B的总效率 = A的效率 + B的效率 = \(1 \div \frac{6}{5} = \frac{5}{6}\)
A和C的总效率 = A的效率 + C的效率 = \(1 \div \frac{3}{2} = \frac{2}{3}\)
B和C的总效率 = B的效率 + C的效率 = \(\frac{1}{2}\)
将这三个式子相加:
\[
2(\text{A的效率} + \text{B的效率} + \text{C的效率}) = \frac{5}{6} + \frac{2}{3} + \frac{1}{2} = 2
\]
\[
\text{A的效率} + \text{B的效率} + \text{C的效率} = 1 \text{ 桶/小时}
\]
三人一起注满这个浴缸所需的时间是1小时。
答案:D