SOLUTION: Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can. If they work together, they can complete the job in 3 hours. Using complete sentences, expla

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Question 913386: Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can. If they work together, they can complete the job in 3 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jimmy to complete this job on his own.
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
1/x+1/(x+8)=1/3
(3*x*(x+8))/x+(3*x*(x+8))/(x+8)=(3*x*(x+8))/3
(3*(x+8))+3*x=x*(x+8)
3*x+24+3*x=x^2+8*x
6*x+24=x^2+8*x
x^2+2*x-24=0
Can it be factored?
What factors of -24 add up to 2?
Nevertheless, we will complete the square
x^2+2*x=24
Add it.
x^2+2*x+(2/2)=24+(2/2)
Square it.
x^2+2*x+(4/4)=24+(4/4)
x^2+2*x+(1)=24+(1)
x^2+2*x+(1)=25
(x+1)^2=25
(x+1)^2=25
We will continue.
x+1=(+-)5.0
x=-1(+-)5.0
Positive useful answer:
x=-1+5.0
One worker is x=4 Harry
x+8=8+4
x+8=12
Other worker =12 Jimmy
check
1/x+1/(x+8)=1/3
1/4+1/(4+8)=1/3
1/4+1/12=1/3
6/24+2/24=1/3
8/24=1/3
1/3=1/3
ok
Useless answer:
x=-1-5.0
Useless answer is x=-6.0
x =-6.0
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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