如果单独完成某项工作，那么甲需要24天，乙需要36天，丙需要48天．现在甲先做，乙后做，最后由丙完成．甲、乙工作的天数比为1：2，乙、丙工作天数比为3：5．问：完成这项工作共用了多

Answer 1

甲：乙=1：2，乙：丙=3：5，则甲：乙：丙=3：6：10．
设完成这项工程共用了x天，可得方程：
(1)/(24)×(3)/(19)x+(1)/(36)×(6)/(19)x+(1)/(48)×(10)/(19)x=1．
           (1)/(152)x+(1)/(114)x+(5)/(456)x=1，
                         (1)/(38)x=1，
                           x=38．
答：完成这项工作共用了38天． (1)/(24)111242424×(3)/(19)x+(1)/(36)×(6)/(19)x+(1)/(48)×(10)/(19)x=1．
           (1)/(152)x+(1)/(114)x+(5)/(456)x=1，
                         (1)/(38)x=1，
                           x=38．
答：完成这项工作共用了38天． (3)/(19)333191919x+(1)/(36)×(6)/(19)x+(1)/(48)×(10)/(19)x=1．
           (1)/(152)x+(1)/(114)x+(5)/(456)x=1，
                         (1)/(38)x=1，
                           x=38．
答：完成这项工作共用了38天． (1)/(36)111363636×(6)/(19)x+(1)/(48)×(10)/(19)x=1．
           (1)/(152)x+(1)/(114)x+(5)/(456)x=1，
                         (1)/(38)x=1，
                           x=38．
答：完成这项工作共用了38天． (6)/(19)666191919x+(1)/(48)×(10)/(19)x=1．
           (1)/(152)x+(1)/(114)x+(5)/(456)x=1，
                         (1)/(38)x=1，
                           x=38．
答：完成这项工作共用了38天． (1)/(48)111484848×(10)/(19)x=1．
           (1)/(152)x+(1)/(114)x+(5)/(456)x=1，
                         (1)/(38)x=1，
                           x=38．
答：完成这项工作共用了38天． (10)/(19)101010191919x=1．
           (1)/(152)x+(1)/(114)x+(5)/(456)x=1，
                         (1)/(38)x=1，
                           x=38．
答：完成这项工作共用了38天． (1)/(152)111152152152x+(1)/(114)x+(5)/(456)x=1，
                         (1)/(38)x=1，
                           x=38．
答：完成这项工作共用了38天． (1)/(114)111114114114x+(5)/(456)x=1，
                         (1)/(38)x=1，
                           x=38．
答：完成这项工作共用了38天． (5)/(456)555456456456x=1，
                         (1)/(38)x=1，
                           x=38．
答：完成这项工作共用了38天． (1)/(38)111383838x=1，
                           x=38．
答：完成这项工作共用了38天．