SOLUTION: a,b, andc can finish a job in 6 days. if b and c work together, the job will take 9 days;if a and c work together, the job will be done in 8 days. in how many days can each man wo

Question 309458: a,b, andc can finish a job in 6 days. if b and c work together, the job will take 9 days;if a and c work together, the job will be done in 8 days. in how many days can each man working alone do the job?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a, b, and c can finish a job in 6 days.
if b and c work together, the job will take 9 days;
if a and c work together, the job will be done in 8 days.
in how many days can each man working alone do the job?
:
Let the completed job = 1
:
"a, b, and c can finish a job in 6 days."
1. + + = 1
:
"if b and c work together, the job will take 9 days;"
2. + = 1
:
"if a and c work together, the job will be done in 8 days."
3. + = 1
:
Multiply eq1 by 3, and eq2 by 2
+ + = 3
+ + = 2
--------------------------subtraction eliminates a & b, find c
18/a = 1
Mult both sides by a
a = 18 hrs alone
:
replace a with 18 in eq3, find c
+ = 1
Multiply by 18c
8c + 18(8) = 18c
8c + 144 = 18c
144 = 18c - 8c
144 = 10c
c =
c = 14.4 hrs alone
:
replace c with 14.4 in eq2, find b
+ = 1
multiply by 14.4b
14.4(9) + 9b = 14.4b
129.6 = 14.4b - 9b
129.6 = 5.4b
b =
b = 24 hrs alone
:
solution: a=18 hrs, b=24 hrs, c= 14.4 hrs
:
See if that flies in the eq1
+ +
.333 + .25 + .417 = 1

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