SOLUTION: 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 lon

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

RELATED QUESTIONS
jimwell and cromwell,working together, can cover the roof of a PNC multipurpose hall in 6 (answered by richwmiller)

Mary can roof their house in 4 days working alone, her husband can roof their house in 6... (answered by josmiceli)

mogaka and onduso working together can do a piece of work in 6 days. mongaka, working... (answered by ikleyn,MathTherapy)

one roofer can put a new roof on a house three times faster than another. Working... (answered by chosenpoint)

one roofer can put a new roof on a house three times faster than another. Working... (answered by edjones)

one roofer can put a new roof on a house three times faster than another. working... (answered by ikleyn)

One roofer can put a new roof on a house three times faster than another. Working... (answered by Theo)

Mary can roof her house in 7 days working alone. Her husband can roof their house in 14... (answered by richwmiller)

Working together Erica and Shawna can answer a days worth of customer-service emails in 4 (answered by josgarithmetic)