SOLUTION: 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 st

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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.
Answer by mananth(16946) About Me  (Show Source):
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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%2F%282%28x-y%29%29%2B18%2F%28x%2By%29=9

21%2F%28%28x-y%29%29%2B39%2F%282%28x%2By%29%29=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