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

Question

2 years ago

6

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.

Mathematics

2 answers:

agasfer [191] · Answer 1 · 2022-07-18T06:45:53+03:00

agasfer [191]2 years ago

8 0

X would be equal to 3 over 1

Elena L [17] · Answer 2 · 2022-07-18T07:48:40+03:00

Answer:

8/3

Step-by-step explanation:

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.