Question 574461
Forward   	40	miles														
Returning speed to DC	20	miles														
																
Forward speed	x			mph												
return speed	x-5	mph												
Total time	=3hours													
Time forward		40	/	x												
time return		20/(x-5)									
																
add up the time =3	hours												
																
40/x	+	20/(x-5)=3				
LCD =	(x)*(x-5)								
multiply the equation by the LCD																
we get																
40*(x-5	)+20x	=	3				
40x-200	+20x=3x^2-15x	
75x-200	=3x^2											
3x^2-75x+200=	0								
3X^2-75	x+200	=	0																							
Find the roots of the equation by quadratic formula																
																
a=	3	b=	-75	c=	200											
																
b^2-4ac=	5625	-	2400													
b^2-4ac=	3225	
{{{sqrt(	3225	)}}}=	56.79								2.99	
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}																
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}																
x1=(	75	+	56.79	)/	6											
x1=	21.96															
x2=(	75	-56.79	) /	6												
x2=	3.04	
Forward speed = 22 mph
return speed = 17 mph