Question 476507
Train 1 7.00 AM --- x kph
Train 2 10.00 AM--- x+15 kph

Distance between two stations = 1080
Midway = 540 km

AT 10.00 AM Train A is 540-3x from A

Distance between them at 10.00AM = 1080-3x
combined speed = x+x+15=2x+15 kph


From 10:00 AM the time taken for them to meet is the same.
Time taken by them to meet = Time taken by Train B to meet

(1080-3x)/(2x+15)= 540/(x+15)
(x+15)(1080-3x)=540(2x+15)
1080x-3x^2+16200 -45x= 1080x+8100
-3x^2-45x+8100=0
3x^2+45x-8100=0
Find the roots of the equation by quadratic formula				
a=	-3	,b=	-45	,c=	8100		
					b^2-4ac=		
b^2-4ac=	2025	-	97200				
b^2-4ac=	99225			
{{{sqrt(	99225	)}}}=	315
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}							
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}							
x1=(	45	+	315	)/	-6		
x1=	-60						
x2=(	45	-315	) /	-6			
x2= 	45						

Train 1 speed = 45 kph which is positive

Train A speed = 45 kph
Train B speed = 60 kph
..
Time taken by train B to meet = 540/60 = 9 hours
Train B starts at 10:00 AM
They meet at 10 + 9 = 19:00 hours OR 7:00 PM

m.ananth@hotmail.ca

m.ananth@hotmail.ca