Question 802147
Jamie recently drove to visit her parents who live 390 miles away. On her way there her average speed was 11 miles per hour faster than on her way home (she ran into some bad weather). If Jamie spent a total of 13 hours driving, find the two rates.

distance = 390 miles
on her way there speed = x mph

time taken = 930/x

On her return speed was x-11 mph

time = 930/(x-11)


Time to go there + time to return = 13 hours

930/x +930/(x-11) = 13

Multiply by x(x-11)

930(x-11)+930x=13x(x-11)

930x-10230+930x=13x^2-143x

Re arrange

13x^2-1860x-143x+10230=0

13x^2-2003x+10230=0

Find the roots of the equation by quadratic formula									
									
a=	13    	b=	-2003	c=	10230		2916		
									
b^2-4ac=	4012009	-	531960						
b^2-4ac=	3480049		{{{sqrt(	3480049	)}}}=	1865.49			
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}									
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}				)/					
x1=(	2003	+	1865.49	)/	26				
x1=	148.79								
x2=(	2003	-	1865.49	)/	26				
x2=	5.29								
Ignore 5.29 									
x	=	148.79	mph	to go there

Return will be 11 mph less