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Question 914459: Jimwell and Cromwell, working together, can cover the roof of a PnC Multipurpose Hall in 6 days. Jimwell, working alone, can complete this job in 5 days less than Cromwell. How long will it take Cromwell to make this job?
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 1/x+1/(x+5)=1/6
(6*x*(x+5))/x+(6*x*(x+5))/(x+5)=(6*x*(x+5))/6
(6*(x+5))+6*x=x*(x+5)
6*x+30+6*x=x^2+5*x
12*x+30=x^2+5*x
x^2-7*x-30=0
Can it be factored?
What factors of -30 add up to -7? (-10, 3)
Nevertheless, we will complete the square
x^2-7*x=30
Add it.
x^2-7*x+(-7/2)=30+(-7/2)
Square it.
x^2-7*x+(49/4)=30+(49/4)
x^2-7*x+(12.25)=30+(12.25)
x^2-7*x+(12.25)=42.25
(x-3.5)^2=42.25
(x-3.5)^2=42.25
We will continue.
x+-3.5=(+-)6.5
x=3.5(+-)6.5
Positive useful answer:
x=3.5+6.5
One worker is x=10
x+5=5+10
x+5=15
Other worker =15
check
1/x+1/(x+5)=1/6
1/10+1/(10+5)=1/6
1/10+1/15=1/6
15/150+10/150=1/6
25/150=1/6
0.16666667=0.16666667
ok
Useless answer:
x=3.5-6.5
Useless answer is x=-3.0
x =-3.0
This answer is useless because it is Negative
For real life cases involving time, distance and other measurements, we reject the negative results
codewtp
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