SOLUTION: a man can row 20 km downstream in the time it takes him to row 8 km upstream. he rows downstream for 1 and 1/2 hours, then turns and rows back for 3 hrs, but he finds that he will

Question 762811: a man can row 20 km downstream in the time it takes him to row 8 km upstream. he rows downstream for 1 and 1/2 hours, then turns and rows back for 3 hrs, but he finds that he will still 3 km from his starting place. find the rate of the man in still water and the rate of the stream.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
a man can row 20 km downstream in the time it takes him to row 8 km upstream. he rows downstream for 1 and 1/2 hours, then turns and rows back for 3 hrs, but he finds that he will still 3 km from his starting place. find the rate of the man in still water and the rate of the stream.
***
let x=rate in still water
let c=rate of stream
(x+c)=rate downstream
(x-c)=rate upstream
travel time=distance/rate
distance=rate*travel time
..

20x-20c=8x+8c
12x=28c
x=28c/12=7c/3
..
1.5(x+c)=3(x-c)+3
1.5x+1.5c=3x-3c+3
-1.5x+4.5c=3
plug in x=7c/3 from first equation
-1.5(7c/3)+4.5c=3
-7c/2+4.5c=3
-3.5c+4.5c=3
c=3
..
-1.5x+4.5*3=3
-1.5x+13.5=3
1.5x=10.5
x=7
rate in still water=7 km/hr
rate of stream=3 km/hr

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