Question 775877
let bus speed =x

bus time = 350/x

Train speed = x-15 km/h

train time= 350/(x-15)

Train takes longer

Train time - bus time = 3/4 hour

{{{350/(x-15)-350/x =3/4}}}

multiply the equation by 4x(x-15)

4x*350-4*350(x-15)=3x(x-15)

1400x-1400x+21000=3x^2-45x


Rearrange
3x^2-45x-21000=0

/3
x^2-15x-7000=0

Find the roots of the equation by quadratic formula							
						
a=	1	,	b=	-15	,	c=	-7000
							
b^2-4ac=	225	+	28000				
b^2-4ac=	28225						
{{{	sqrt(	28225	)=	168	}}}		
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}							
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}							
x1=(	15	+	168	)/	2		
x1=	91.50						
{{{x2=(-b-sqrt(b^2-4ac))/(2a)}}}							
x2=(	15	-168	) /	2			
x2=	-76.50						
Ignore negative value							
bus   	speed	91.50	km/h