SOLUTION: A boat travels 2 km upstream and 2km back. The time for the round trip is 4hrs. The speed of the stream is 4km/hr. What is the speed of the boat in still water?

Question 442293: A boat travels 2 km upstream and 2km back. The time for the round trip is 4hrs. The speed of the stream is 4km/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 2 km upstream and 2km back. The time for the round trip is 4hrs. The speed of the stream is 4km/hr. What is the speed of the boat in still water?
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Upstream DATA:
distance = 2 km; rate = b-4 km ; time = 2/(b-4)hrs
---------------------------
Downstream DATA:
distance = 2 km ; rate = b+4 km ; time = 2/(b+4) hrs
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Equations:
time + time = 4 hrs
2/(b-4) + 2/(b+4) = 4
---
Multiply thru by (b-4)(b+4)
2(b+4) + 2(b-4) = 4b^2-64
4b = 4b^2-64
b^2-b-16 = 0
---
b = [1 +- sqrt(1-4*1*-16)]/2
----
b = [1 +- sqrt(65)]/2
----
Positive solution:
b = [1+sqrt(65)]/2 = 4.53 km/hr (speed in still water)
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Cheers,
Stan H.
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