SOLUTION: Can someone help me solve this word problem? The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hrs.

Question 204081: Can someone help me solve this word problem?
The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hrs. What is the speed of the boat in still water?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hrs. What is the speed of the boat in still water?
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Upriver DATA:
distance = 40 miles ; rate = b-5 ; time = d/r = 40/(b-5) hrs.
--------------------------
Downriver DATA:
distance = 40 miles ; rate = b+5 ; time = 40/(b+5) hrs
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Equation:
time up + time down = 6 hrs
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40/(b-5) + 40/(b+5) = 6
---
Multiply thru by (b-5)(b+5) to get:
40(b+5) + 40(b-5) = 6(b^2-25)
80b = 6b^2 - 150
6b^2 - 80b - 150 = 0
3b^2 - 40b - 75 = 0
(b-15)(3b+5) = 0
Positive solution:
b = 15 mph (speed of the boat in still water)
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Cheers,
Stan H.
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