HMMT 二月 2005 · GEN2 赛 · 第 3 题
HMMT February 2005 — GEN2 Round — Problem 3
题目详情
- 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?
解析
- 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 paints z 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 , and z + x = 1 / 6 . Adding all three equations and dividing by 2 gives x + y + z = 3 / 8 . So, working together, the three folks can paint 3 / 8 houses in a day, or 8 / 3 days per house. 1