SOLUTION: please help me solve this problem in quadratic equation; 1.a motorboat takes 4 hours to travel 30 miles downstream and then 18 miles upstream on a river whose current flows at the

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: please help me solve this problem in quadratic equation; 1.a motorboat takes 4 hours to travel 30 miles downstream and then 18 miles upstream on a river whose current flows at the      Log On


   

Question 154461: please help me solve this problem in quadratic equation;
1.a motorboat takes 4 hours to travel 30 miles downstream and then 18 miles upstream on a river whose current flows at the rate of 3 miles per hour. How fast can the boat travel in still water?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1.a motorboat takes 4 hours to travel 30 miles downstream and then 18 miles upstream on a river whose current flows at the rate of 3 miles per hour. How fast can the boat travel in still water?
Let "b" be the speed of the boat in still water.
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Upstream DATA:
distance = 18 miles ; rate = b-3 ; time = d/r = 18/(b-3) hrs.
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Downstream DATA:
distance = 30 miles ; rate = b+3 ; time = d/r = 30/(b+3) hrs
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EQUATION:
time up + time down = 4 hrs
18/(b-3) + 30/(b+3) = 4
18(b+3) + 30(b-3) = 4(b^2-9)
18b + 54 + 30b - 90 = 4b^2 - 36
4b^2 - 48b = 0
b^2 - 12 = 0
Positive solution:
b = sqrt(12) = 3.464 mph (speed of the boat in still water)
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Cheers,
Stan H.