SOLUTION: The current of a river is 2 miles per hour. A boat travels to a point 8 miles upstream and back again in 3 hours.
What is the speed of the boat in still water?
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What is the speed of the boat in still water?
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Question 419040: The current of a river is 2 miles per hour. A boat travels to a point 8 miles upstream and back again in 3 hours.
What is the speed of the boat in still water? Found 3 solutions by mananth, ikleyn, timofer:Answer by mananth(16949) (Show Source):
Time upstream + time downstream = 3hours
t=d/r
............
16/(x+2)+16/(x-2)=3
LCD = (x-2)(x +2)
16*(x-2)+16(x+2)=3
16x-32+ 16x+32=3(X^2-4)
32x=3X^2-12
3X^2-32 x-12=0
Use the quadratic formula
b^2-4ac= 1168
x=(32+sqrt(1168))/6
11.03 mph speed in still water
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The current of a river is 2 miles per hour. A boat travels to a point 8 miles upstream and back again in 3 hours.
What is the speed of the boat in still water?
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The solution and the answer in the post by @mananth both are incorrect.
I came to bring a correct solution.
speed in still water = x mph.
current speed 2 mph.
upstream speed = x-2 mph.
downstream speed = x+2 mph.
Distance = 8 miles.
Time equation
+ = 3 .
LCD = (x-2)*(x+2)
8*(x-2) + 8*(x+2) = 3
8x - 16+ 8x + 16 = 3(x^2-4)
16x = 3x^2 - 12
3x^2 - 16x - 12=0
Use the quadratic formula
b^2 - 4ac = (-16)^2 - 4*3*(-12) = 256 + 144 = 400
x =
Use positive root = = 6.
ANSWER. The speed of the boat in still water is 6 mph.
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