Question 514279
Boat speed	x	mph														
current speed 	5	mph														
																
Distance with current	36	miles														
Distance against current	12	miles														
																
spee with current	x	+	5	mph												
spee against  current=	x		-5	mph												
Total   time =		9	hours													
Time with current=		36	/(	x	+	5	)									
time against current 		12	/	(	x	-5	)									
																
Time with  current + time against  =			9	hours												
																
36/(x +	5 )	+	12	/(x	-5	)	=	9				
LCD =	(	x	+	5	)*	(x	-5	)								
multiply the equation by the LCD																
we get																
3*(x	-5)+	12	(x	+5)=	9	(x^2		-25	)
36)x	-180	+	 12	x	+	60	)	=	9	X^2		-225			
48	x	-120	=	9	X^2		-225									
9	X^2	-48	x	120	+	-225	=	0								
9	X^2+	-48	x+	-105	=	0										
/	9															
1	X^2	-5.33	x	-11.67	=	0										
																
	Find the roots of the equation by quadratic formula															
																
	a=	1	,b=	-5.33	,c=	-11.67										
																
	b^2-4ac=	28.41	+	46.68												
	b^2-4ac=	75.09														
	{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}							49.98								
	{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}															
	{{{x1=(-12+21)/(12)}}}															
	x1=(	5.33	+	8.67	)/	2										
	x1=	7										7      				
	x2=(	5.33	-8.67	) /	2											
	x2= 	-1.67														
	Ignore negative value															
	Boat speed	=	7	mph