241.One project ,A needs 12hours to finish it alone,while B needs 15hours to finish it alone.After A and B working together for an hour ,then A works an hour,B works an hour.A and B turn down like this .So how many hours does the project need?

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241.One project ,A needs 12hours to finish it alone,while B needs 15hours to finish it alone.After A and B working together for an hour ,then A works an hour,B works an hour.A and B turn down like this .So how many hours does the project need?
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241.One project ,A needs 12hours to finish it alone,while B needs 15hours to finish it alone.After A and B working together for an hour ,then A works an hour,B works an hour.A and B turn down like this .So how many hours does the project need?
241.One project ,A needs 12hours to finish it alone,while B needs 15hours to finish it alone.After A and B working together for an hour ,then A works an hour,B works an hour.A and B turn down like this .So how many hours does the project need?

241.One project ,A needs 12hours to finish it alone,while B needs 15hours to finish it alone.After A and B working together for an hour ,then A works an hour,B works an hour.A and B turn down like this .So how many hours does the project need?
小学的题.
翻译如下:一项工程,A独自完成需要12小时,B独自完成需要15小时.
A和B共同工作1小时后,A独自工作一小时,然后B独自工作一小时
这样轮流下去,完成这项工程需要多少个小时?
A的工作效率是1/12,B的工作效率是1/15,也就是说A、B一小时完成的分别占总工程的1/12和1/15
这样A、B共同工作一小时完成的量是1/12+1/15=3/20
那么就还剩下17/20的工程量让A、B来轮流完成
惊奇地发现17/20=5*(1/12+1/15)+1/10
也就是说A、B这样轮流了5次之后 再轮回到A来做再做总工程的1/10就可以完成了
所以需要的时间是:1+2*5+(1/10)/(1/12)=12.2

不是一个整数,答案是11.2小时。
顺便说一下,如果还有这样的问题还可以来找我

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