HMMT 二月 2005 · GEN2 赛 · 第 3 题

英文解析

3. Working together, Jack and Jill can paint a house in 3 days; Jill and Joe can paint the same house in 4 days; or Joe and Jack can paint the house in 6 days. If Jill, Joe, and
   Jack all work together, how many days will it take them?
   Solution: 8 / 3
   Suppose that Jack paints x houses per day, Jill paints y houses per day, and Joe paintsz houses per day. Together, Jack and Jill paint 1 / 3 of a house in a day — that is,
   x + y = 1 / 3 .
   Similarly,
   y + z = 1 / 4 ,
   z + x = 1 / 6 .and
   Adding all three equations and dividing by 2 givesx + y + z = 3 / 8 .
   So, working together, the three folks can paint 3 / 8 houses in a day, or 8 / 3 days perhouse. 1