SOLUTION: The current in a stream moves at a speed of 3mph. A boat travels 45 miles upstream and 45 miles downstream in a total time of 8 hours. What is the speed of the boat in still wate

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The current in a stream moves at a speed of 3mph. A boat travels 45 miles upstream and 45 miles downstream in a total time of 8 hours. What is the speed of the boat in still wate      Log On


   

Question 131830This question is from textbook Introductory Algebra
: The current in a stream moves at a speed of 3mph. A boat travels 45 miles upstream and 45 miles downstream in a total time of 8 hours. What is the speed of the boat in still water?
Any help would be greatly appreciated on this! This question is from textbook Introductory Algebra

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The current in a stream moves at a speed of 3mph. A boat travels 45 miles upstream and 45 miles downstream in a total time of 8 hours. What is the speed of the boat in still water?
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Let the speed of the boat in still water be "b"
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Upstream DATA:
Distance = 45 miles ; Rate = b-3 mph ; Time = d/r = 45/(b-3) hrs.
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Downstream DATA:
Distance = 45 miles ; Rate = b+3 mph ; Time = d/r = 45/(b+3) hrs
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EQUATION:
time + time = 8 hrs
45/(b-3) + 45/(b+3 = 8
45(b+3) + 45(b-3) = 8(b^2-9)
90b = 8b^2-72
8b^2-90b-72 = 0
(b-12)(8b+6)=0
Positive Solution:
b=12 mph (boat speed in still water)
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Cheers,
Stan H.