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

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) (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.

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