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 take 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.

Logic
Sep 14, 2018

#1**+2 **

3x^2 = 4(16 - 4x), solve for x

Solve for x:

3 x^2 = 4 (16 - 4 x)

Expand out terms of the right hand side:

3 x^2 = 64 - 16 x

Subtract 64 - 16 x from both sides:

3 x^2 + 16 x - 64 = 0

The left hand side factors into a product with two terms:

(x + 8) (3 x - 8) = 0

Split into two equations:

x + 8 = 0 or 3 x - 8 = 0

Subtract 8 from both sides:

x = -8 or 3 x - 8 = 0

Add 8 to both sides:

x = -8 or 3 x = 8

Divide both sides by 3:

** x = 8/3 =2 2/3 miles per hour.**

Guest Sep 14, 2018