SOLUTION: Ashraf and Bahar together can do a piece of work in 12 days, which Bahar and Charles together can do in 16 days . After Ashraf has been working at it 5 days and Bahar for 7 days Ch

Question 480916: Ashraf and Bahar together can do a piece of work in 12 days, which Bahar and Charles together can do in 16 days . After Ashraf has been working at it 5 days and Bahar for 7 days Charles finishes in 11 days .In how many days Charles will do the work?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Ashraf and Bahar together can do a piece of work in 12 days, which Bahar and Charles together can do in 16 days . After Ashraf has been working at it 5 days and Bahar for 7 days Charles finishes in 11 days .In how many days Charles will do the work?
**
let a=days Ashraf can do the job alone
1/a=His work rate
..
let b=days Bahar can do the job alone
1/b=His work rate
..
let c=days Charles can do the job alone
1/c=His work rate
..
Sum of individual work rates= work rate working together
1) 1/a+1/b=1/12
2) 1/c+1/b=1/16
working separately to complete the job:
3) 5/a+7/b+11/c=1
..
multiply eq1 by 7
4) 7/a+7/b=7/12
3) 5/a+7/b+11/c=1
subtract
5) 2/a-11/c=-5/12
..
multiply eq2 by 7
6) 7/c+7/b=7/16
3) 5/a+7/b+11/c=1
subtract
7) -5/a-4/c=-9/16
..
multiply eq5 by 5
8) 10/a-55c=-25/12=-100/48
multiply eq7 by 2
9) -10/a-8/c=-18/16=-54/48
add eq8 and eq9
-63/c=-154/48
c=63*48/154=19.64 days (rounded)
..
ans:
Charles would take 19.64 days to complete the job working alone
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