SOLUTION: speed of boat in still water is 18km/h it takes 1/2hour extra in going 12km upstream instead of going the same distance downstream find speed of stream

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Question 957831: speed of boat in still water is 18km/h it takes 1/2hour extra in going 12km upstream instead of going the same distance downstream find speed of stream
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
speed of boat in still water is 18km/h it takes 1/2hour extra in going 12km upstream instead of going the same distance downstream find speed of stream
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Upstream DATA:
dist = 12 km ; time = t + (1/2) hrs ; rate = d/t = 12/(2t+1)/2 = 24/(2t+1) kph
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Downstream DATA:
dist = 12 km ; time = t hrs ; rate = 12/t kph
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Equations:
Upstream:: 24/(2t+1) = 18-s
Downstream:: 12/t = 18+s
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Modify and solve:
s = [12/t]-18
Substitute::
24/(2t+1) = 18-[(12/t)-18]
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24/(2t+1) = 36-(12/t)
24 = 36(2t+1)-(12/t)(2t+1)
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24 = 72t + 36 - [24+12/t)]
-12 = 72t - 24 - 12/t
12/t - 72t +12 = 0
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1/t - 6t + 1 = 0
-6t^2 +t + 1 = 0
(-2t+1)(3t+1) =
Positive solution:
t = 1/2
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Solve for "s":
s = [12/t]-18
stream speed = (12/(1/2) - 18 = 24-18 = 6 km/hr
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Cheers,
Stan H.
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