SOLUTION: 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

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Question 149216: 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 nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
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?
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Let S = speed of patrol boat in still water
and T = time traveled going up river
.
(S-3)T = 60
(S+3)(9-T) = 60
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(S+3)(9-T) = 60
9S+27-ST-3T = 60
.
(S-3)T = 60
T = 60/(S-3)
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9S+27-ST-3T = 60
9S+27-S(60/(S-3))-3(60/(S-3)) = 60
9S(S-3)+27(S-3)-S(60)-3(60) = 60(S-3)
9S^2-27S+27S-81-60S-180 = 60S-180
9S^2-27S+27S-81-60S = 60S
9S^2-81-60S = 60S
9S^2-81-120S = 0
9S^2 - 120S - 81 = 0
3S^2 - 40S - 27 = 0
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At this point, you must either factor or apply the quadratic formula. In this case, you can only apply the quadratic formula. It will give you two answers -- one negative and one positive. Since, a negative speed won't make sense here, the only one that makes sense is the positive answer.
S = 13.98 mph
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See below for the details:
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1924 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 13.9772373998204, -0.643904066487103. Here's your graph:
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