Question 593458
Let james take x hours to do the job alone.
He does 1/x of the job in 1 hour

Colleen takes x-2 hours

she does 1/(x-2) of the job in 1 hour

Together they take 10 hours
They do 1/10 of the job in 1 hour

{{{(1/x)+ (1/(x-2)) = 1/10 }}}

LCD = x(x-2)

Multiply the equation by the LCD

{{{(x-2) +x = x(x-2)/10 }}}

10x-20 +10x = x^2-2x

x^2-2x-20x+20=0

x^2-22x+20=0

Find the roots of the equation by quadratic formula								
								
a=	1	,	b=	-22	,	c=	20	
								
b^2-4ac=	484	+	-80					
b^2-4ac=	404		
{{{	sqrt(	404	)=	20.1	}}}
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}								
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}								
x1=(	22	+	20.1	)/	2			
x1=	21.05							
x2=(	22	-20.1	) /	2				
x2=	0.95			
0.95 is not 	possible

James takes 21 hours to do the job alone