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.

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.

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keshavgandhi04 keshavgandhi04 · Answer 2 · 2021-12-01T12:38:01+01:00

The value of x = 8/3 and this can be determined by forming the quadratic equation using the given data and then factorizing it.

Given :

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.
x > 0

The quadratic equation that represents the given situation is:

[tex](x^2)\times 3 = (16-4x)\times 4[/tex]

Simplify the above quadratic equation.

[tex]3x^2= 64-16x[/tex]

[tex]3x^2+16x - 64=0[/tex]

Now, factorize the above equation.

[tex]3x^2+24x-8x - 64=0[/tex]

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

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

x = -8 will be rejected because x is always positive. So, the value of x = 8/3.

For more information, refer to the link given below:

https://brainly.com/question/11897796