SOLUTION: a and b can do a piece of work in 18 days, b and c can do it in 24 days while c and a can finish it in 36 days . In how many days can a,b,c finish it, if they all work together?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: a and b can do a piece of work in 18 days, b and c can do it in 24 days while c and a can finish it in 36 days . In how many days can a,b,c finish it, if they all work together?      Log On


   

Question 812829: a and b can do a piece of work in 18 days, b and c can do it in 24 days while c and a can finish it in 36 days . In how many days can a,b,c finish it, if they all work together?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
I know I solved this a few days ago but here we go again.
18/a+18/b=1,
24/b+24/c=1,
36/a+36/c=1,
x/a+x/b+x/c=1
a = 48, b = 144/5, c = 144, x = 16
16 days for a b and c
another way
1/a+1/b =1/18,
1/b+1/c=1/24,
1/a+ 1/c=1/36,
2/a+2/b+2/c=1/8
1/a+1/b+1/c=1/x
x=16