SOLUTION: A and B can do a piece of work in 6 days,B and c together in 10 days,c and A together in 7 1/2 days.in how many days can c individually completes the work?

Question 975770: A and B can do a piece of work in 6 days,B and c together in 10 days,c and A together in 7 1/2 days.in how many days can c individually completes the work?

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A and B can do a piece of work in 6 days,B and c together in 10 days,c and A together in 7 1/2 days.in how many days can c individually completes the work?
***
let x=number of days A can individually complete the work
1/x=his work rate
let y=number of days B can individually complete the work
1/y=his work rate
let z=number of days C can individually complete the work
1/z=his work rate
..
1/x+1/y=1/6 (A & B)
1/z+1/y=1/10 (C & B)
1/x+1/z=1/7 (A & C)
..
1/x+1/y=1/6
1/z+1/y=1/10
subtract:
1/x-1/z=1/6-1/10=10/60-6/60=4/60=1/15
1/x-1/z=1/15
..
1/x-1/z=1/15
1/x+1/z=1/7
subtract:
-2/z=1/15-1/7=7/105-15/105-8/105
8z=2*105=210
z=210/8=26.25
How many days can C individually completes the work? 26.25
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