Question 173348
the current in a stream moves at a speed of 3mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hours. What is the speed of the boat in still water? 
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Upstream DATA:
distance  45 miles; rate = b-3 mph ; time = 45/(b-3)
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Downstream DATA:
distance = 45 miles ; rate = b+3 mph ; time = 45/(b+3)
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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
Use the quadratic formula whenever you cannot see the factors:
b = [90 +- sqrt(8100 - 4*8*-72)]/16
b = [90 +- sqrt(10404)]/16
b = [90 +-102]/16
Positive solution:
b = 192/16 = 12 mph (speed of the boat in still water)
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Cheers,
Stan H.