Final answer:
To establish the equation for the relationship between Melanie's distance and time cycled, additional information on her cycling rate is needed; otherwise, it's not possible to determine the correct choice among the provided equations.
Step-by-step explanation:
The equation that represents the relationship between Melanie's distance d and the time t cycled must take into account the rate at which she cycles. If this rate is constant, we can use the formula d = vt, where v is the velocity and t is the time. Based on the provided solutions for t, which are 3.96 s and -1.03 s, we can determine that the negative value for time does not make sense in a physical context since negative time would imply an event happening before the start of motion. Consequently, we only consider t = 3.96 s as the valid solution. Now, to find the corresponding equation among the choices provided, we would need to know the initial distance d0 and velocity v. However, without additional information regarding the velocity or the initial distance, we cannot conclusively determine which option A) d = t, B) d = 2t, C) d = 0.5t, or D) d = 3t is correct. More data about Melanie's rate of cycling would be required to select the appropriate equation.