一项工程,甲独做所需天数是乙丙合作的a倍,乙独做所需天数是甲丙合作的b倍,丙独做所需天数是甲乙合作的c倍
1个回答

甲乙丙所需天数分别是x,y,z,根据已知有

x = a(y+z),a = x / (y+z),a+1 = (x+y+z) / (y+z)

y = b(x+z),b = y / (x+z),b+1 = (x+y+z) / (x+z)

z = c(x+y),c = z / (x+y),c+1 = (x+y+z) / (x+y)

所以

1/(a+1) + 1/(b+1) + 1/(c+1)

= (y+z) / (x+y+z) + (x+z) / (x+y+z) + (x+y) / (x+y+z)

= (y+z + x+z + x+y) / (x+y+z)

= 2

相关问题