SOLUTION: If A,B and C work together on a job, it will take 1 and 1/3 hours. If only A and B work, it would take 1 and 5/7 hours, but if B and C work, it would take 2 and 2/5 hours. How long

Algebra ->  Linear-equations -> SOLUTION: If A,B and C work together on a job, it will take 1 and 1/3 hours. If only A and B work, it would take 1 and 5/7 hours, but if B and C work, it would take 2 and 2/5 hours. How long      Log On


   

Question 208065This question is from textbook modern college algebra
: If A,B and C work together on a job, it will take 1 and 1/3 hours. If only A and B work, it would take 1 and 5/7 hours, but if B and C work, it would take 2 and 2/5 hours. How long it would take each man, working alone to complete the job?
A and B working together can do a job in 6 hours. A become ill after 3 hours of working with B, and B finished the job, continuing to work alone in 8 hours. How long would it take each working alone to do the job? This question is from textbook modern college algebra

Found 2 solutions by ankor@dixie-net.com, vipower:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If A,B and C work together on a job, it will take 1 and 1/3 hours. If only A and B work, it would take 1 and 5/7 hours, but if B and C work, it would take 2 and 2/5 hours. How long it would take each man, working alone to complete the job?
:
Change 1 & 1/3 hrs to 4%2F3
Let the completed job = 1
:
Simplify the shared work equations
%284%2F3%29%2FA + %284%2F3%29%2FB + %284%2F3%29%2FC = 1 >> 4%2F%283A%29 + 4%2F%283B%29 + 4%2F%283C%29 = 1 >> 4%2FA + 4%2FB + 4%2FC = 3
:
convert 1 & 5/7 hrs to 12%2F7
%2812%2F7%29%2FA + %2812%2F7%29%2FB = 1 >> 12%2F%287A%29 + 12%2F%287B%29 = 1 >> 12%2F%28A%29 + 12%2F%28B%29 = 7
:
Multiply 1st equation by 3 and subtract the 2nd equation
12%2FA + 12%2FB + 12%2FC = 9
12%2FA + 12%2FB + 0%2FC = 7
---------------------eliminates A & B, find C
12%2FC = 2
12 = 2C
C = 6 hrs alone
:
The 3rd equation we can use decimal: 2 & 2/5 hrs = 2.4 hrs
2.4%2FB + 2.4%2FC = 1
Replace C with 6, find B
2.4%2FB + 2.4%2F6 = 1
2.4%2FB + .4 = 1
2.4%2FB = 1 -.4
2.4%2FB = .6
.6B = 2.4
B = 2.4%2F.6
B = 4 hrs alone
:
Find A, using the 2nd equation
12%2FA + 12%2F4 = 7
12%2FA + 3 = 7
12%2FA = 7 - 3
12%2FA = 4
4A = 12
A = 3 hrs alone
:
:
Check solution in the 1st equation using a calc
%284%2F3%29%2F3 + %284%2F3%29%2F4 + %284%2F3%29%2F6 =
:
:
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A and B working together can do a job in 6 hours. A become ill after 3 hours of working with B, and B finished the job, continuing to work alone in 8 hours. How long would it take each working alone to do the job?
:
Working the same together equation:
6%2FA + 6%2FB = 1
:
Working when one gets sick equation: (B works a total of 11 hrs)
3%2FA + 11%2FB = 1
:
Multiply the above equation by 3 and subtract the 1st equation
6%2FA + 22%2FB = 2
6%2FA + 6%2FB = 1
-----------------------------eliminates A
16B = 1
B = 16 hrs alone
:
Find A using the 1st equation
6%2FA + 6%2F16 = 1
6%2FA = 16%2F16 - 6%2F16
6%2FA = 10%2F16
Cross multiply
10A = 6 * 16
10A = 96
A = 9.6 hrs alone
;
:
Check solution on a calc using the "sick equation"
3%2F9.6 + 11%2F16 = 1

Answer by vipower(2) About Me  (Show Source):
You can put this solution on YOUR website!
thanks a lot