In the equation \( d = 0.5 + 5t \), the total distance \( d \) that Jillian travels is determined by her jogging time \( t \). Here, \( t \) is the independent variable because it is the variable you can control (the amount of time she jogs), and \( d \) is the dependent variable because it depends on that jogging time.
Thus, the correct answer is: The independent variable is time and the dependent variable is distance.