SOLUTION: The Hudson River flows at a rate of 3 mile 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?

Question 149899This question is from textbook
: The Hudson River flows at a rate of 3 mile 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? This question is from textbook

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The Hudson River flows at a rate of 3 mile 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 x = speed of patrol boat in still water
.
Time it takes to go up river:
60/(x-3)
.
Time it takes to go down river:
60/(x+3)
.
Therefore, we have:
60/(x-3) + 60/(x+3) = 9
multiplying both sides by (x-3)(x+3) we get:
60(x+3) + 60(x-3) = 9(x-3)(x+3)
60x + 180 + 60x - 180 = 9(x^2-9)
120x = 9x^2 - 81
0 = 9x^2 - 120X - 81
0 = 3x^2 - 40X - 27
.
Since we can't factor, we must use the quadratic equation. The solutions it gives is a positive and a negative answer. Since it can't be negative we use the positive one.
.
x = 14 mph
.
Quadratic solution follows:

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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