Question

初二数学 急（4）某工程,甲队独做所需的天数是乙、丙两队合作所需天数的a倍；乙队独做所需天数是甲、丙两队合作所需天数的b

Answer 1

设甲、乙、丙单独做各需xyz天

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

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

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

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

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

=2((x+y+z)/(x+y+z)

=2