SOLUTION: three skilled laborers a,b,c together can do construction job in 20 days a & b could do the job in 30 days b & c could do the job in 40 dyas. how long would it take each to do the

Question 224473: three skilled laborers a,b,c together can do construction job in 20 days a & b could do the job in 30 days b & c could do the job in 40 dyas. how long would it take each to do the job alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
three skilled laborers a,b,c together can do construction job in 20 days a & b
could do the job in 30 days b & c could do the job in 40 days.
how long would it take each to do the job alone?
:
Write a "shared work" equation for each statement
:
"three skilled laborers a,b,c together can do construction job in 20 days"
Let the completed job = 1.
= 1
:
" a & b could do the job in 30 days"
= 1
:
" b & c could do the job in 40 days"
= 1
:
how long would it take each to do the job alone?
:
We can use elimination here:
Multiply the 1st equation by 2, subtract the 3rd equation
= 2
___ = 1
--------------------------------
= 1
a = 40 days alone
:
Replace a with 40 in the 2nd equation
= 1
= 1
= 1 -
=
multiply both sides by 4b
4(30) = b
b = 120 days alone
:
Find c using the 3nd equation, replace b with 120
= 1
= 1
=
=
Multiply both sides by 3c
3(40) = 2c
120 = 2c
c =
c = 60 days alone
:
Solutions: a = 40 days, b = 120 days, c = 60 days
;
:
Check this using the 1st equation
= 1
+ + = 1
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