Question 785816
A boat travels 16 1/2 miles
upstream and 18 miles downstream
in 9 hrs. It then travels 21 miles
upstream and
19 1/2 miles downstream in 11 hrs.
Find the rate of the crew in still
water and that of the stream.

speed of boat x
speed of current y 

16 1/2/(x-y) +18/(x+y)=9

{{{33/(2(x-y))+18/(x+y)=9}}}


{{{21/((x-y))+39/(2(x+y))=11}}}

Let 1/(x-y) =a and 1/(x+y)=b

33a/2 + 18b=9
multiply by 2
33a+36b=18.......................(1)

21a+39b/2 =11
multiply by 2
42a+39b=22.......................(2)


33.00	a	+	36.00	b    	=	18.00	.............1	
Total value								
42.00	a	+	39.00	b    	=	22.00	.............2	
Eliminate	y							
multiply (1)by		-39.00						
Multiply (2) by		36.00						
-1,287.00	a		-1,404.00	b    	=	-702.00		
1,512.00	a	+	1,404.00	b    	=	792.00		
Add the two equations								
225.00	a				=	90.00		
/	225.00							
a	=	0.40						
plug value of			a	in (1)				
33.00	a	+	36.00	b    	=	18.00		
13.20		+	36.00	b    	=	18.00		
			36.00	b    	=	18.00		-13.20
			36.00	b    	=	4.80		
				b    	=	0.13		

1/(x-y)=0.4
1/(x+y)=0.13

x-y = 2.5
x+y=7.69

2x=10.2
x=5.1 mph  speed of boat
y=2.6 mph  speed of current