Question

Carlo,Clyde,and Marky working together can do a job in 6 days. Carlo and Marky can do can do the job in 8 days. Clyde and Marky can do the job in 9 days. find how long it will take each guy working alone to do the job.

Answer 1

marko's rate --- 1/x
carlo's rate --- 1/y
clyde's rate --- 1/z

combined rate of all three
= (xy + xz + yz)/(xyz)
xyz/(xy + xz + yz) = 6
xyz = 6((xy + xz + yz) **

Carlo and Marko
1/(1/x + 1/y) = 8
xy/(x+y) = 8
xy = 8(x+y) ***

clyde and marko
1/(1/x + 1/z) = 9
xz = 9(x+z) ****

that's a messy set of equations,
ran it through Wolfram and got this

http://www.wolframalpha.com/input/?i=solve+xyz+%3D+6(xy+%2B+xz+%2B+yz)+,+xy+%3D+8(x%2By)+,+xz+%3D+9(x%2Bz)