We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

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