Question 718095
speed upstream = x
speed downstream = y

time = distance/time

Time upstream + time down stream = 13 hours

40/x +45/y = 13

let 1/x =a and 1/y =b

40a+45b =13................(1)

Similarly
30/x +27/y 9

30a+27b=9..................(2)


40	a	+	45	b 	=	13	.............1	
Total value								
30	a	+	27	b 	=	9	.............2	
Eliminate	y							
multiply (1)by		-3						
Multiply (2) by		5						
-120	a		-135	b 	=	-39		
150	a	+	135	b 	=	45		
Add the two equations								
30	a				=	6		
/	30							
a	=	  1/ 5						
plug value of			a	in (1)				
40	a	+	45	b 	=	13		
8		+	45	b 	=	13		
			45	b 	=	13		-8
			45	b 	=	5		
				b 	=	  1/ 9		
a=	  1/ 5
therefore x=5	speed upstream	
b=	  1/ 9	
y=9 speed downstream

so speed of boat = 7 km/h
speed of current = 2 km/h