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

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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

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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

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b = [1 +- sqrt(1-4*1*-16)]/2

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b = [1 +- sqrt(65)]/2

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Positive solution:

b = [1+sqrt(65)]/2 = 4.53 km/hr (speed in still water)