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Question 407455: If it takes workers A and B 2 days to complete a job. And it takes workers B and C 3 days to complete the same job. And it takes workers A and C 4 days to complete this job how long does it take each worker to do this job alone. And what formulas are used.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! If it takes workers A and B 2 days to complete a job.
And it takes workers B and C 3 days to complete the same job.
And it takes workers A and C 4 days to complete this job how long does it take
each worker to do this job alone.
:
Let a, b, c, represent the time required by each work alone
:
Let the completed job = 1
:
Write a shared work equation for each statement:
:
"If it takes workers A and B 2 days to complete a job."
 +  = 1
:
"If it takes workers B and C 3 days to complete the same job."
 +  = 1
:
"it takes workers A and C 4 days to complete this job"
 +  = 1
:
Add all three equations to give us another equation to work with
+ +  = 1
 + + = 1
+  + = 1
---------------------------------------
 +  +  = 3
:
Multiply the 1st equation by 3, subtract the above equation from it
+  + = 3
+ + = 3
---------------------------------------subtraction eliminates a
+  - = 0
:
=
Cross multiply
c = 7b
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In equation: + = 1, replace c with 7b
+  = 1
Multiply by 7b, results
7(3) + 3 = 7b
21 + 3 = 7b
24 = 7b
b = 
b = 3.43 hrs, B alone
:
Find c
c = 7b
c = 7(3.43)
c = 24 hrs, C alone
:
Find a using, + = 1; replace c with 24
+  = 1
multiply by 24a
24(4) + 4a = 24a
96 = 24a - 4a
96 = 20a
a = 
a = 4.8 hrs, A alone
:
:
Check this in the 1st equation
 +  = 1
.42 + .58 = 1 confirms our solutions of:
:
A = 4.8 hrs, B = 3.43 hrs, C = 24 hrs (almost useless)
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