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Question 906764: Jessie and Mark are planning to paint a house together. Jessie thinks that if he works alone, it would take him 5 hours more than the time Mark takes a paint the entire house. Working together, they can complete the job in 6 hours.
*What equation represents the situation?
*How long would it take Jessie and Mark if each work alone in painting the entire house?
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 1/j+1/m=1/x
j=m+5
1/(m+5)+1/m=1/6
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
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 can continue
x-3.5=+-6.5
x=3.5+-6.5
Positive useful answer:
x=3.5+6.5
One answer is x=10
x+5=5+10
x+5=15
check
1/x+1/(x+5)=1/6
1/10+1/(10+5)=1/6
1/10+1/15=1/6
6/60+4/60=1/6
10/60=1/6
1/6=1/6
ok
Negative useless answer:
x=3.5-6.5
Negative answer is x=-3.0
For real life cases involving time, distance and other measurements, we reject the negative results
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