Question 526467
Returning to DC speed = x mph
Going to Bethesda x-5 mph

Distance between them is 30 miles

Time going to bethseda + time returning to Dc = 4.5 hours

t=d/r

15/x + 15/(x-5)= 4.5 hours

LCD = x(x-5)

Multiply by LCD 

15(x-5)+15x=4.5 * x(x-5)
15x-75+15x=4.5x^2-22.5x

4.5x^2-52.5x+75=0
multiply by 2
9x^2-105x+150=0
/3
3x^2-35x+50=0

Find the roots of the equation by quadratic formula								
								
a=	3	,	b=	-35	,	c=	50	
								
b^2-4ac=	1225	+	-600					
b^2-4ac=	625		{{{	sqrt(	625	)=	25	}}}
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}								
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}								
x1=(	35	+	25	)/	6			
x1=	10.00							
x2=(	35	-25	) /	6				
x2= 	1.67							


x=10 
Speed returning = 10 mph
Speed while going is 5 mph
m.ananth@hotmail.ca