SOLUTION: 4. The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still wa

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Question 155379: 4. The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water?
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
# 4

Let x = speed of boat in still water



Start with the distance-rate-time formula



Plug in and . This equation represents the upstream journey


Divide both sides by to isolate "t"


So the expression for the time it takes to go upstream can be represented by the expression

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Plug in and . This equation represents the downstream journey


Divide both sides by to isolate "t"


So the expression for the time it takes to go downstream can be represented by the expression


Now simply add the two time expressions to get:


Now set that expression equal to the total time of 9 hours


Multiply every term by the LCD to clear the denominators


FOIL


Distribute


Subtract from both sides. Add to both sides.


Combine like terms


Notice we have a quadratic equation in the form of where , , and


Let's use the quadratic formula to solve for x


Start with the quadratic formula


Plug in , , and


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


or Break up the expression.


So the answers are or


which approximate to or


Since a negative speed doesn't make sense in this problem, this means that the only solution is

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Answer:

So the speed of the boat in still water is approximately 13.98 mph (rounded to the nearest hundredth).
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