SOLUTION: Please help me translate this into a quadratic equation and solve.
The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in
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Question 139175: Please help me translate this into a quadratic equation and solve.
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 ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
he 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?
:
Let s = speed of the boat in still water
:
(s-3) = speed upstream
(s+3) = speed downstream
:
Write a time equation; Time = dist/speed
:
Time upstream + time downstream = 9 hr
+ = 9
:
multiply equation by (s-3)(s+3) to get rid of the denominators:
(s-3)(s+3)* + (s-3)(s+3)* = 9(s-3)(s+3)
:
60(s+3) + 60(s-3) = 9(s^2 - 9)
:
60s + 180 + 60s - 180 = 9s^2 - 81
:
120s = 9s^2 - 81
:
0 = 9s^2 - 120s - 81
:
Simplify, divide equation by 3, giving us a simple quadratic equation
3s^2 - 40s - 27 = 0
:
We need to use the quadratic formula to solve for s: a=3; b=-40; c=-27
:
The positive solution = 13.977 ~ 14 mph
:
:
Check solution using 14 mph
60/17 + 60/11 =
3.529 + 5.454 = 8.983 ~ 9 hrs
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