SOLUTION: I need help with this word problem: The instructions are to use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real
Question 144531: I need help with this word problem: The instructions are to use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to find the roots; just determine the number and types of solutions.
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?
You can put this solution on YOUR website! The instructions are to use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to find the roots; just determine the number and types of solutions.
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?
:
Translate the equation into a quadratic equation:
:
Let x = speed in still water
then
(x+3) = speed downstream
and
(x-3) = speed upstream
:
Write a time equation, Time = dist/speed
:
Time up + time down = 9 hrs + = 9
Multiply equation by (x-3)(x+3) and you have;
:
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; a quadratic equation a=9, b=-12, c=-81
The discriminant: b^2 - 4*a*c
:
-120^2 + (4 * 9 * -81)
14400 - (-2916) is > 0; therefore it has two real roots
