SOLUTION: A boat travels 7 km upstream and 7km back. The time for the round trip is 4 hrs. The speed of the stream is 3 ​km/hr. What is the speed of the boat in still​ water?
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Question 1071692: A boat travels 7 km upstream and 7km back. The time for the round trip is 4 hrs. The speed of the stream is 3 km/hr. What is the speed of the boat in still water? Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! A boat travels 7 km upstream and 7km back. The time for the round trip is 4 hrs. The speed of the stream is 3 km/hr. What is the speed of the boat in still water?
Upstream DATA:
dist = 7 km ; time = t hrs ; rate = 7/t km/hr
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Downstream DATA:
dist = 7 km ; time = 4-t hrs ; rate = 7/(4-t) km/hr
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Rate Equations:
b - 3 = 7/t
b + 3 = 7/(4-t)
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Solve for "t"::
[7/t]+3 = [7/(4-t)]-3
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7/(4-t) - 7/t = 6
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[7t-7(4-t)]/(4t-t^2) = 6
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14t-28 = 24t - 6t^2
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6t^2 - 10t - 28 = 0
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3t^2 - 5t -14 = 0
t = 3.15 hrs
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Solve for "b":
b-3 = 7/t
b = 7/3.15 + 3
boat speed = 5.22 km/hr
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Cheers,
Stan H.
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