One day, I decide to run to the park. On the way there, I run at a rate of x^2 miles per hour for 3 hours. On the way back, I ta
ke the same path and jog at a slower rate of 16 - 4x miles per hour so that it takes me 4 hours to get home. Given that x > 0, what is x? Express your answer as a common fraction.
Since we know that the distance that I traveled to the park and the distance that I traveled to get back home are the same, and that distance = rate x time, we have that
(x^2)(3)=(16-4x)(4)
3x^2=64-16x
3x^2+16x-64=0
(3x-8)(x+8)=0
Solving this equation, we get the solutions x=8/3 and x=-8. Since x must be positive, we have x=8/3.
The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
