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Quiz when eating moon cake

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一次,诺贝尔经济学获奖者数学家约翰·纳什参加一个数学年会,会间休息的时候,有人就给他出了一道数学题。有甲、乙两人分别从两个地点出发往中间走,这两个地点相距 20公里,甲、乙两人的速度都是每小时10公里。甲还带了一条狗,这条狗的速度是每小时30公里,它先是和甲一起出发向乙走,遇到乙后就折返向甲走,遇到甲后再折返向乙走,如此反复直到甲、乙在中间会合。现在问当甲、乙在中间会和时,狗走了多远。

Two people (guy A and guy B), who are 20 km away from each other, are walking toward each other, at 10 km per hour. There is a dog, which goes at 30 km per hour. She (the dog) started with the guy A first. Because she goes faster than A, so she will meet B on the way. When she meet the B, she will turn around to run toward A, and so on,…until A and B meet. The question is: how much distance did the dog take before A meet B?