SOLUTION: meralda is kayaking in the grand river which has a downstream flow (current) of 1 mile per hor. She paddles 5 miles downstream and then turns around and paddles 6 miles upstream, t

Question 1070433: meralda is kayaking in the grand river which has a downstream flow (current) of 1 mile per hor. She paddles 5 miles downstream and then turns around and paddles 6 miles upstream, the trail takes 3 hours how fast can she paddle in still water?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
speed*time=distance
paddling speed in still water is x mph
x+1*t=5
coming back is 3-t hours
(x-1)*(3-t)=6
t=5/(x+1)
(3-t)=6/(x-1)
t=3-[6/(x-1)]
Set the t s equal to each other
5/(x+1)=3-[6/(x-1)]=(3x-3-6)/(x-1)=(3x-9)/(x-1)
cross-multiply
5x-5=(3x-9)(x+1)=3x^2-6x-9
0=3x^2-11x-4
(3x+1)(x-4)=0
positive root only, x=4 mph in still water ANSWER
check
downstream at 5mph takes 1 hour
upstream at 3 mph takes 2 hours
adds to 3 hours.
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