Question 914753
Plane speed	x	mph											
wind speed 	50	mph											
													
Distance with wind	1200	miles											
Distance against wind	1000	miles											
													
spee with wind	x	+	50	mph									
speed against	x		50	mph									
Total   time =		4	hours										
Time with current=		1200	/(	x	+	50	)						
time against current		1000	/	(	x	-50	)						
													
Time with  current + time against  =			4	hours									
													
1200	/(	x	+	50	)	+	1000	/(x	-50	)	=	4	
LCD =	(	x	+	50	)*	(x	-50	)					
multiply the equation by the LCD													
we get													
1200	*	(x	-50	)+	1000	(x	+	50	)=	4	(x^2-	2500	)
1200	x	-60000	+	1000	x	+	50000	)=	4	X^2		10000	
2200	x	0	=	10	X^2		-10000						
4	X^2	-2200	x	0	+	-10000	=	0					
4	X^2+	-2200	x+	-10000	=	0							
/	1												
4	X^2	-2200	x	-10000	=	0							
													
	Find the roots of the equation by quadratic formula												
													
	a=	4    	b=	-2200    	c=	-10000    							
													
	b^2-4ac=	4840000    	-	-160000    									
	b^2-4ac=	5000000    			{{{sqrt(	5000000    	)}}}=	2236 1/9					
	{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}												
	{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}												
	x1=(	2200    	+	2236 1/9	)/	8    							
	x1=	554 1/2											
	x2=(	2200    	-2236 1/9	) /	8    								
	x2=	-4 1/2											
	Ignore negative value			mph									
	x	=	554 1/2