Question 140876: A,B,and C can finish a job in six days. If B and C work together, the job will take 9 days; if A and C work together, the job will take 8 days. In how many days can each man working alone do the job?
Found 2 solutions by ankor@dixie-net.com, josmiceli:
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 six days. If B and C work together, the job will take 9 days; if A and C work together, the job will take 8 days. In how many days can each man working alone do the job?
:
Let the completed job = 1
write 3 equations
 +  +  = 1
:
 +  = 1
:
 +  = 1
:
Use elimination: mult the eq1 by 3, and eq2 by 2:
 +  +  = 3
 + + = 2
----------------------------------------- Subtraction eliminates B & C, Find A
= 1
A = 18 days by himself
:
Use elimination: mult the eq1 by 4, and eq3 by 3:
 +  +  = 4
+  + = 3
----------------------------------------- Subtraction eliminates A & C, Find B
24/B = 1
B = 24 days by himself
:
Use eq2, substitute 24 for B, find C
 + = 1
Multiply equation by 24C
9C + 24(9) = 24C
216 = 24C - 9C
216 = 15C
C = 
C = 14.4 days by himself
;
Check solutions in eq1
 +  +  =
.333 + .250 + 4.17 = 1
Answer by josmiceli(19441)  (Show Source):
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