Question 725505
Michelle take x hours for 1 job

Michelle does 1/x of the job in 1 hour
Shawn takes x+12 hours
Shawn does 1/(x+12) of the job in 1 hour

together they complete {{{(1/x)+1/(x+12) }}} of the job in 1 hour

They take 14.4 hours to do the job together

they do 1/14.4 of the job in 1 hour


{{{(1/x)+1/(x+12) = 1/14.4}}}

{{{(1/x)+1/(x+12) = 5/72}}}

multiply by 72x(x+12)

72(x+12)+72x=5x(x+12)

72x+864+72x=5x^2+60x

5x^2-84x-864=0


Find the roots of the equation by quadratic formula							
							
a=	5	,	b=	-84	,	c=	-864
							
b^2-4ac=	7056	+	17280				
b^2-4ac=	24336						
{{{	sqrt(	24336	)=	156	}}}		
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}							
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}							
x1=(	84	+	156	)/	10		
x1=	24.00						
{{{x2=(-b-sqrt(b^2-4ac))/(2a)}}}							
x2=(	84	-156	) /	10			
x2=	-7.20						
Ignore negative value							
x=	24	

Now you know how many hours Shawn will take			
							
m.ananth@hotmail.ca