Question 179618: 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 hours. What is the speed of the boat in still water?
I have figured the distance is 40 miles with a speed of r-5 upstream and r in still water, and the total time is 6 hours but I still can not figure out how to write the equation and solve it.
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 hours. 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)
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Downriver DATA:
distance = 40 miles : rate = b + 5 ; time = 40/(b+5)
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Equation:
time + time = 6 hrs
40/(b-5) + 40/(b+5) = 6
40(b+5) + 40(b-5) = 6(b^2-25)
80b = 6b^2 - 150
Rearrange:
3b^2 - 40b -150 = 0
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positive solution:
b = [40 + sqrt(40^2 - (4*3*-150)]/6
b = 23.05 mph (boat speed in still water)
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Cheers,
Stan H.
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