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 - x 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.
Speed = distance/time
distance = speed *time
Use this formula to find the distance on the way there,
and then again to find the distance on the way back.
Then put the 2 distances equal and solve the arising equation.
Try it yourself, if you get stuck then show what you have done and ask for more assistance.