奥数题:如果甲先做1小时,然后乙接替甲做1小时

  • 时间:2020-04-29 11:52:54
  • 分类:数学世界
  • 阅读:153 次

奥数题:一项工程,甲独做需9小时,乙独做需12小时。如果甲先做1小时,然后乙接替甲做1小时,再由甲接替乙做1小时……两人如此交替工作,完成这项工程需要多少小时?

数学题解答

甲每小时做:1÷9=1/9
乙每小时做:1÷12=1/12
甲和乙一小时一共做:1/9+1/12=7/36
5小时一共做:7/36 × 5 = 35/36     (轮流做的话,实际上一共需要10小时)
还剩下:1 - 35/36 =1/36 这时轮到甲做
甲还要做:1/36 ÷ 1/9 = 1/4(小时)
一共需要的时间:5×2 + 1/4 = 10又1/4(小时)

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