SOLUTION: Jenny can cut and split a cord of firewood in 3 fewer hours than Tim can. When they work together it takes them 2 hours. How long would it take each of them to do the job alone?

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Question 914924: Jenny can cut and split a cord of firewood in 3 fewer hours than Tim can. When they work together it takes them 2 hours. How long would it take each of them to do the job alone?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
1/x+1/(x+3)=1/2
(2*x*(x+3))/x+(2*x*(x+3))/(x+3)=(2*x*(x+3))/2
(2*(x+3))+2*x=x*(x+3)
2*x+6+2*x=x^2+3*x
4*x+6=x^2+3*x
x^2-1*x-6=0
Can it be factored?
What factors of -6 add up to -1?
Nevertheless, we will complete the square
x^2-1*x=6
Add it.
x^2-1*x+(-1/2)=6+(-1/2)
Square it.
x^2-1*x+(1/4)=6+(1/4)
x^2-1*x+(0.25)=6+(0.25)
x^2-1*x+(0.25)=6.25
(x-0.5)^2=6.25
(x-0.5)^2=6.25
We will continue.
x+-0.5=(+-)2.5
x=0.5(+-)2.5
Positive useful answer:
x=0.5+2.5
One worker is x=3
x+3=3+3
x+3=6
Other worker =6
check
1/x+1/(x+3)=1/2
1/3+1/(3+3)=1/2
1/3+1/6=1/2
6/18+3/18=1/2
9/18=1/2
0.5=0.5
ok
Useless answer:
x=0.5-2.5
Useless answer is x=-2.0
x =-2.0
This answer is useless because it is Negative
For real life cases involving time, distance and other measurements, we reject the negative results
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