Answer:
Gene can take 0.8 hours to complete work
Step-by-step explanation:
Gene can paint a room in x hours
We are given that Marilyn can paint it in 1 hour less time than Gene
Marilyn can paint a room in (x-1) hours
Gene 1 hour work = [tex]\frac{1}{x}[/tex]
Marilyn 1 hour work =[tex]\frac{1}{x-1}[/tex]
(Gene and Marilyn)'s 1 day work together= [tex]\frac{1}{x}+\frac{1}{x-1}[/tex]
Together they can do the job in 4 hours.
So, their 1 hour work = [tex]\frac{1}{4}[/tex]
So, [tex]\frac{1}{x}+\frac{1}{x-1}=\frac{1}{4}[/tex]
[tex]\frac{x-1+x}{x(x-1)}=\frac{1}{4}[/tex]
[tex]4(2x-1)=x^2-x[/tex]
[tex]8x-4=x^2-x[/tex]
[tex]x^2-x-8x+4=0[/tex]
[tex]x^2-9x+4=0[/tex]
General equation : [tex]ax^2+bx+c=0[/tex]
Formula : [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{9\pm\sqrt{(-9)^2-4(1)(4)}}{21}[/tex]
[tex]x=\frac{9\pm\sqrt{(-9)^2-4(1)(4)}}{21}[/tex]
x=0.812,0.0446
So, Gene can take 0.8 hours to complete work
