Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the distance formula for traveling in terms of speed, time, and distance?

1. d = rt

2. r = d/t

3. t = d/r

4. All of the above

The correct answer is: All of the above

The distance formula, which relates distance, speed (rate), and time, can be expressed in various ways, demonstrating the interconnectedness of these three variables. The fundamental relationship is encapsulated in the formula \(d = rt\), where \(d\) represents distance, \(r\) represents speed, and \(t\) represents time. This equation shows that distance is the product of speed and time, which is essential in calculating how far something travels given its speed and the duration of travel. Additionally, rearranging this formula leads to other forms, such as \(r = d/t\), which expresses speed as distance divided by time, and \(t = d/r\), which calculates time as distance divided by speed. Each of these formulas can be derived from the basic \(d = rt\) equation, reinforcing the concept that they are all valid expressions of the same relationship. Thus, the answer that states "All of the above" is correct because it acknowledges the validity of all three expressions, illustrating the flexibility and interdependence of speed, time, and distance in solving related problems. By understanding these relationships, one can effectively apply them in various mathematical scenarios involving motion.