Question

the following situation involves a rate of change that is constant. write a statement that describes how one variable changes with respect to the other, give the rate of change numerically (with units), and use the rate of change rule to answer any questions. you run along a path at a constant speed of 2.3 miles per hour. how far do you travel in 1.1 hours? in 3.3 hours? which statement describes this situation? a. the distance traveled varies with respect to time with a rate of change of 2.3 mi/h. b. the distance traveled varies with respect to time with a rate of change of 2.3 h/mi. c. time varies with respect to distance traveled with a rate of change of 2.3 mi/h. d. time varies with respect to distance traveled with a rate of change of 2.3 h/mi.

Explanation:

To determine the correct statement, we analyze the relationship between distance, time, and speed. Speed is the rate of change of distance with respect to time. The formula for distance is \( d = v \times t \), where \( v \) is speed (2.3 mi/h) and \( t \) is time.

• Option A is too vague as it doesn't mention the rate.
• Option B: Distance (dependent variable) changes with time (independent variable) at a rate equal to speed (2.3 mi/h), which matches \( d = 2.3t \).
• Option C: The rate here would be \( \frac{1}{2.3}\approx0.43 \) h/mi, not 2.3 h/mi, and time doesn't vary with distance at 2.3 h/mi.
• Option D: The rate of time with respect to distance is \( \frac{1}{v}=\frac{1}{2.3}\approx0.43 \) h/mi, not 2.3 h/mi.

So, Option B correctly describes the situation.

Answer:

B. The distance traveled varies with respect to time with a rate of change of 2.3 mi/h.