Question 864657
Plane	speed	x   	mph		Time forward + time return = hours			2	hours								
wind  	speed	25	mph														
																	
against	wind  	x-	25	mph													
with	wind  	x+	25	mph													
																
Distance=	150	miles															
																	
Time against + time with  =			2	hours													
t=d/r																	
																	
150	/(	x   	+	25	)	+	150	/(x	-	25	)	=	2				
																	
LCD =	(x	-	25	)	(	x   	+	25	)								
150	*(	x   	-	25	)	+	150	(x	+	25	)	=	2	(x^2	-	625	)
150	x   	-	-3750	+	150	x   	+	3750		=	2	(	x ^2		-	625	)
300	x   	=	2	x ^2		-1250											
2	x ^2	-	-300	x   	-	1250	=	0									
																	
Find the roots of the equation by quadratic formula																	
																	
a=	2	,	b=	-300	,	c=	1250										
																	
b^2-4ac=	90000	+	-10000														
b^2-4ac=	80000																
{{{	sqrt(	80000	)=	282.84	}}}												
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}																	
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}																	
x1=(	300	+	282.84	)/	4												
x1=	145.71																
{{{x2=(-b-sqrt(b^2-4ac))/(2a)}}}																	
x2=(	300	-282.84	) /	4													
x2=	4.29																
																	
Plane	speed	145.7	mph														
																	
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