PREP关于效率的题 屡做屡错~ 大家帮帮忙啊！！！！

Lambton

Pumps A, B and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours;  pumps A and C, operating simultaneously, can fill the tank in 3/2 hours;  and pumps B and C, operating simultaneously, can fill the tank in 2 hours.  How many hours does it take pumps A, B, and C,  operating simultaneously, to fill the tank?

A. 1/3
B. 1/2
C. 2/3
D. 5/6
E. 1


答案是 E）1

请各位指教啊！！

Avengeryzc

a+b=5\6   b+c=1\2   a+c=2\3   3个式子相加  2(a+b+c)=1  
so a+b+c=1

ZKRAP

设总工作量为1
a b c分别为每小时A B C 的工作速度
1/(a+b)=6/5   1/(a+c)=3/2   1/（b+c)=2
联立三个方程式 求出a b c
最后1/(a+b+c)=1
即三个一起工作时间为1小时。

azuo1209

你可以这么想。此工作是1
Pumps A and B, operating simultaneously, fill a certain tank in 6/5 hours;
那么AB 的速度就是 5/6,
同理：AC=2/3,BC=1/2,
ABC的速度就是 1/2 (5/6+2/3+1/2)= 1
so, ABC 一起就是 1/1 =1

jake1

就是关系式列出全相加，即A+B=5/6, A+C=2/3, B+C =1/2，三式相加为2(A+B+C)=2,则1/A+B+C = 1

Lambton

太感谢大家了 终于会做这种类型的题了！！！
跪谢跪谢！！