SOLUTION: At his usual rate a man rows 15 miles downstream in five hours less time than it takes him to return. If he doubles his usual rate, the time downstream is only one hour less than t

Question 547099: At his usual rate a man rows 15 miles downstream in five hours less time than it takes him to return. If he doubles his usual rate, the time downstream is only one hour less than the time upstream. Find the rate of the streams current?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let speed of boat be x
speed of current be y
downstream speed = x+y
upstream speed = x-y
15/(x-y) -15/(x+y)=5
LCD = (x+y)(x-y)
multiply by the LCD
15(x+y)-15(x-y)=5(x^2-y^2)
15x+15y-15x+15y=5(x^2-y^2)
30y=5(x^2-y^2)
----------------
Speed is doubled
downstream speed = 2x+y
upstream speed = 2x-y
15/(2x-y)-15/(2x+y)=1
LCD = (2x+y)(2x-y)
multiply by the LCD
15(2x+y)-15(2x-y)=4x^2-y^2
30x+15y-30x+15y=4x^2-y^2
30y=4x^2-y^2
equate 30y from both equations
5x^2-5y^2=4x^2-y^2
x^2-4y^2=0
x=2y
substitute x=2y in
15/(x-y) -15/(x+y)=5
15/(2y-y)-15/(2y+y)=5
15/y-15/3y=5
45-15=15y
30=15y
30/15=y
y=2 the current speed
x=4 mph boat speed
m.ananth@hotmail.ca

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