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?

Algebra ->  Rate-of-work-word-problems -> 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?      Log On


   

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) About Me  (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,
12%2FA + 12%2FB = 1
:
B and C can do it in 15 days and
15%2FB + 15%2FC = 1
;
C and A can do the same work in 20 days.
20%2FA + 20%2FC = 1
:
Use elimination; Mult the 1st eq by 5, mult the 3nd eq by 3
60%2FA + 60%2FB = 5
60%2FA + 60%2FC = 3
------------------------------Subtraction eliminates A, leaving us with
60%2FB - 60%2FC = 2
:
Multiply the 2nd equation by 4, add to the above equation
60%2FB - 60%2FC = 2
60%2FB + 60%2FC = 4
-------------------------------addition eliminates C, find B
120%2FB = 6
120 = 6B
B = 120%2F6
B = 20 hrs working alone
:
Use the 2nd equation to find C, substitute 20 for B, find C
15%2F20 + 15%2FC = 1
Multiply by 20C, results:
15C + 20(15) = 20C
15C + 300 = 20C
300 = 20C - 15C
5C = 300
C = 300%2F5
C = 60 hrs working alone
:
Use the 3rd equation to find A
20%2FA + 20%2F60 = 1
Multiply by 60A
60(20) + 20A = 60A
1200 = 60A - 20A
40A = 1200
A = 1200%2F40
A = 30 hrs working alone
:
Summarize: A=30; B=20; C=60
;
:
Check it in the 1st equation
12%2FA + 12%2FB = 1
12%2F30 + 12%2F20 =
4%2F10 + 6%2F10 = 1
:
YOu can confirm it in the other two equations.