<PRE><B>Question 730994</B>
First Part	60	km													
Second Part	24	km													
															
First Part	x			mph											
Second Part	x		-4	mph											
Total time		8	hours												
First Part	time 	60	/	x											
Second Part	time 	24	/	(	x	-4	)								
															
Time first part + time second part =			8	hours											
															
60	/	x		+	24	/(x	-4	)	=	8					
LCD =	(	x)*	(x	-4	)							
multiply the equation by the LCD															
we get															
								=	8			
60	x	-240	+	)+	24		x		=	8	X^2			-32	x
116	x-240	=	8	X^2		=	0							
8	X^2	-116	x+	240			=	0							
8	X^2+	-116	x+	240	=										
/	8														
8	X^2	-116	x+	240	=0										
															
Find the roots of the equation by quadratic formula															
															
a=	8    	b=	-116	c=	240										
															
b^2-4ac=	13456	-	7680												
b^2-4ac=	5776		{{{sqrt(	5776	)}}}=	76				OK					5
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}															
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}				)/											
x1=(	116	+	76	)/	16										
x1=	12														
x2=(	116	-	76	)/	16										
x2=	2.5														
Ignore 2.5															
x	=	12	kph												</PRE>