Final answer:
To find the value of t when d = -5 for an inverse variation where d = 20 when t = 2, we calculate the constant k as 40 and then find t by dividing k by d, giving us t = -8.
Step-by-step explanation:
If d varies inversely as t, this means that when t increases, d decreases, and vice versa, according to the inverse variation formula d = k/t, where k is a constant. Given that d = 20 when t = 2, we can find the constant k by multiplying these two values together, giving us k = 40. To find the value of t when d=-5, we rearrange the formula to t = k/d and substitute in the values to get t = 40 / (-5) = -8.
Since t represents time, a negative value would normally be unreasonable, as time cannot be negative in most real-world scenarios. However, as the question provides options with negative values and no context is given that discounts them, we consider the mathematical result without applying physical constraints.
Thus, the correct answer is D) -8.