Question 536708
Forward speed    	x			mph											
Return speed	x		25	mph											
Total time		3.5	hours												
Time forward		150	/	x											
Time return		150	/	(	x	25	)								
															
Time first part + time second part =			3.5	hours											
															
150	/	x				+	150	/(x	25	)	=	3.5			
LCD =	x	(x	+25	)							
multiply the equation by the LCD															
we get															
150	*	(x	25	)+	150		x				=	3.5			
150	x	3750	+	150	x				=	3.5	X^2		+	87.5	x
212.5	x	3750	=	3.5	X^2										
3.5	X^2	-212.5	x	-3750			=	0							
3.5	X^2+	-212.5	x+	-3750	=										
/	3.5														
1	X^2	-60.71	x	-1071.43	=										
															
Find the roots of the equation by quadratic formula															
															
a=	1	b=	-60.71	c=	-1071.43										
															
b^2-4ac=	3686.22	-	4285.71												
b^2-4ac=	7971.9{{{sqrt(	7971.94	)}}}=	89.29								
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}															
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}															
x1=(	60.71	+	89.29	)/	2										
x1=	75		    												
x2=(	60.71	-89.29	) /	2											
x2= 	-14.29		-14 2/7												
Ignore negative value															
x	=	75	kph	

Returning speed = 100 kph

m.ananth@hotmail.ca