Let's analyze the given equation:
[tex]\[
\frac{10}{r} = t
\][/tex]
Here, [tex]\( t \)[/tex] represents the time it will take Corey to hike the trail, and [tex]\( r \)[/tex] represents the rate at which Corey hikes (in kilometers per hour).
### Independent Variable:
The independent variable is the variable that can be changed or controlled in an experiment to observe its effect on the dependent variable. In this case, the rate [tex]\( r \)[/tex] is the value that can be changed. Corey can choose to hike at different speeds (rates), making [tex]\( r \)[/tex] the independent variable.
### Dependent Variable:
The dependent variable is the variable that depends on the value of the independent variable. In this case, the time [tex]\( t \)[/tex] depends on the rate [tex]\( r \)[/tex]. As Corey changes the hiking rate, the time taken to complete the trail will change accordingly. Therefore, [tex]\( t \)[/tex] is the dependent variable.
### Conclusion:
- Dependent Variable: Time [tex]\( t \)[/tex]
- Independent Variable: Rate [tex]\( r \)[/tex]
Hence, the dependent variable is [tex]\( t \)[/tex] (Time), and the independent variable is [tex]\( r \)[/tex] (Rate).
