SOLUTION: Word Problem: Working alone, Bill can finish the job one hour faster than Adam. It would take Carl three times as long as Bill to do the job alsone. Working together, it takes t

Question 151218: Word Problem: Working alone, Bill can finish the job one hour faster than Adam. It would take Carl three times as long as Bill to do the job alsone. Working together, it takes them 1 hour. How long would it take each of them to finish the job if they wre working alone? (Hint if you don't use the LCD, this problem might have cubes which would be nearly unsolvable.)
Found 2 solutions by scott8148, ankor@dixie-net.com:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
"Working alone, Bill can finish the job one hour faster than Adam" __ A=B+1

"It would take Carl three times as long as Bill to do the job alone" __ C=3B

"Working together, it takes them 1 hour" __ [1/A]+[1/B]+[1/C]=1

substituting __ [1/(B+1)]+[1/B]+[1/(3B)]=1 __ multiplying by 3B(B+1) (the LCD) __ [3B]+[3(B+1)]+[B+1]=3B(B+1)

3B+3B+3+B+1=3B^2+3B __ 0=3B^2-4B-4 __ factoring __ 0=(3B+2)(B-2)

0=3B+2 __ -2/3=B __ negative value not realistic

0=B-2 __ 2=B __ so A=3 and C=6
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Working alone, Bill can finish the job one hour faster than Adam. It would take Carl three times as long as Bill to do the job alone. Working together, it takes them 1 hour. How long would it take each of them to finish the job if they were working alone?
:
Let a, b, c = each guy's time working alone
Let the completed job = 1
;
The equation
+ + = 1
:
Write an equation from each statement:
"Bill can finish the job one hour faster than Adam."
a = (b+1)
:
" It would take Carl three times as long as Bill to do the job alone".
c = 3b
:
Substitute for a & c in the original equation, find b:
+ + = 1
multiply equation by 3b(b+1) and you have
:
3b + 3(b+1) + (b+1) = 3b(b+1)
:
3b + 3b + 3 + b + 1 = 3b^2 + 3b
:
7b + 4 = 3b^2 + 3b
:
0 = 3b^2 + 3b - 7b - 4
;
A quadratic equation:
3b^2 - 4b - 4 = 0
Factors to:
(3b + 2)(b - 2) = 0
The positive solution
b = 2 hrs for Bill working alone
then
2+1 = 3 hrs for Adam working alone
and
3(2) = 6 hrs for Carl working alone
:
Check solution in original equation
+ + =
+ + = 1
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