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 4.6 miles per hour. how far do you travel in 1.7 hours? in 3.9 hours?

which statement describes this situation?

a. time varies with respect to distance traveled with a rate of change of 4.6 mi/h.
b. the distance traveled varies with respect to time with a rate of change of 4.6 mi/h.
c. time varies with respect to distance traveled with a rate of change of 4.6 h/mi.
d. the distance traveled varies with respect to time with a rate of change of 4.6 h/mi.

what is the distance traveled after 1.7 hours?
7.82 miles
(type an integer or a decimal.)

what is the distance traveled after 3.9 hours?
miles
(type an integer or a decimal.)

Explanation:

Identify variables and rate of change

Using the Independent and Dependent Variables and Rate of Change Interpretation knowledge points, we identify the variables. Time is the independent variable, and distance traveled is the dependent variable. The rate of change is the constant speed of \(4.6\text{ mi/h}\). Therefore, the distance traveled varies with respect to time with a rate of change of \(4.6\text{ mi/h}\).

Calculate distance after 1.7 hours

Using the Rate of Change Rule knowledge point, we calculate the distance traveled by multiplying the rate of change by the elapsed time:

$$ \text{Distance} = 4.6\text{ mi/h} \times 1.7\text{ h} = 7.82\text{ miles} $$

Calculate distance after 3.9 hours

Using the Rate of Change Rule knowledge point, we calculate the distance traveled for the second time interval:

$$ \text{Distance} = 4.6\text{ mi/h} \times 3.9\text{ h} = 17.94\text{ miles} $$

Answer:

Question 1

• (A) Time varies with respect to distance traveled with a rate of change of 4.6 mi/h.
• (B) The distance traveled varies with respect to time with a rate of change of 4.6 mi/h. (Correct answer)
• (C) Time varies with respect to distance traveled with a rate of change of 4.6 h/mi.
• (D) The distance traveled varies with respect to time with a rate of change of 4.6 h/mi.

Question 2

\(7.82\)

Question 3

\(17.94\)