SOLUTION: .A and B can do a piece of work in 12 days,B and C can do it in 15 days and C and A can do the same work in 20 days. How long would each take to complete the job?

Question 268391: .A and B can do a piece of work in 12 days,B and C can do it in 15 days and C and A can do
the same work in 20 days. How long would each take to complete the job?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let the piece of work = 1
:
Write a shared work equation for each phrase:
:
A and B can do a piece of work in 12 days,
+ = 1
:
B and C can do it in 15 days and
+ = 1
;
C and A can do the same work in 20 days.
+ = 1
:
Use elimination; Mult the 1st eq by 5, mult the 3nd eq by 3
+ = 5
+ = 3
------------------------------Subtraction eliminates A, leaving us with
- = 2
:
Multiply the 2nd equation by 4, add to the above equation
- = 2
+ = 4
-------------------------------addition eliminates C, find B
= 6
120 = 6B
B =
B = 20 hrs working alone
:
Use the 2nd equation to find C, substitute 20 for B, find C
+ = 1
Multiply by 20C, results:
15C + 20(15) = 20C
15C + 300 = 20C
300 = 20C - 15C
5C = 300
C =
C = 60 hrs working alone
:
Use the 3rd equation to find A
+ = 1
Multiply by 60A
60(20) + 20A = 60A
1200 = 60A - 20A
40A = 1200
A =
A = 30 hrs working alone
:
Summarize: A=30; B=20; C=60
;
:
Check it in the 1st equation
+ = 1
+ =
+ = 1
:
YOu can confirm it in the other two equations.
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