Final answer:
Formulas I (d=50t) and III (d=rt) represent direct variation of distance with time, as both are in the form of distance equaling a constant rate times time.
Step-by-step explanation:
The question asks which distance formula or formulas show d as direct variation with t. Recall that direct variation means as one variable changes, the other changes at a constant rate, which can be described by a formula of the type y = kx, where k is a constant. Analyzing the provided formulas:
- Formula I: d=50t suggests that distance (d) varies directly with time (t) by a constant rate of 50.
- Formula II: d=1672 shows a constant distance, no matter the value of t, which means this is not a variation.
- Formula III: d=rt also suggests direct variation because it's in the form of d = (constant rate) × t.
Hence, the correct answer is formulas I and III, which shows that distance varies directly with time. This corresponds to option c, I and III.