Question 734136
A boat travels 7 km upstream and 7km back. The time for the round trip is 10 hours. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?

let speed in still water = x km/h

with current x+4 km/h

against current speed = x-4 km/h

time up + time return = 10

7/(x+4)+7/(x-4)=10

multiply equation by (x+4)(x-4)

7(x-4)+7(x+4)= 10(x^2-16)

7x-28+7x+28 = 10x^2-160

14x=10x^2-160

10x^2-14x-160=0

/2
5x^2-7x-80=0


Find the roots of the equation by quadratic formula								
								
a=	5	,	b=	-7	,	c=	-80	
								
b^2-4ac=	49	+	1600					
b^2-4ac=	1649							
{{{	sqrt(	1649	)=	40.61	}}}			
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}								
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}								
x1=(	7	+	40.61	)/	10			
x1=	4.76							
{{{x2=(-b-sqrt(b^2-4ac))/(2a)}}}								
x2=(	7	-40.61	) /	10				
x2=	-3.36							
Ignore negative value								
boat   	speed	4.761	kph