Question

a team from the department of public works is painting lines on the freeway. the number of hours needed to finish the project depends on the length of road that needs to be lined.
h = the number of hours needed
r = the length of road
which of the variables is independent and which is dependent?
h is the independent variable and r is the dependent
r is the independent variable and h is the dependent

Explanation:

To determine independent and dependent variables, we analyze the relationship: the number of hours \( h \) needed to finish the project depends on the length of the road \( r \) (since a longer road would take more hours). An independent variable is the one that is manipulated or does not depend on others, while a dependent variable depends on the independent one. Here, \( r \) (road length) is independent (it can vary freely, and we observe how \( h \) changes with it), and \( h \) (hours) is dependent (it depends on \( r \)).

Answer:

r is the independent variable and h is the dependent variable