Question 547099
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)
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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