SOLUTION: The current in a stream moves at a speed of 3 mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hr. What is the speed of the boat in still water?

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Question 172939This question is from textbook Introductory Algebra
: The current in a stream moves at a speed of 3 mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hr. What is the speed of the boat in still water? This question is from textbook Introductory Algebra

Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
The current in a stream moves at a speed of 3 mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hr. What is the speed of the boat in still water?
.
You will need to apply the "distance" formula:
d = rt
where
d is distance
r is rate or speed
t is time
.
Solving for t:
d = rt
d/r = t
.
Let x = speed of boat in still water
45/(x+3) + 45/(x-3) = 8
Multiplying both sides by:(x+3)(x-3)
45(x-3) + 45(x+3) = 8(x+3)(x-3)
45[(x-3) + (x+3)] = 8(x^2-9)
45[2x] = 8x^2-72
90x = 8x^2-72
0 = 8x^2-90x-72
0 = 4x^2-45x-36
.
Since we can't factor, we solve with the quadratic equation. Doing so will yield:
x = {12, -0.75}
.
We can ignore the negative solution leaving us with
x = 12 mph (speed of boat in still waters)
.
Details of quadratic 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=2601 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 12, -0.75. Here's your graph: