To analyze the relationship between time (t) and distance (d) for a train traveling at a constant speed, we can use the equation:
\[ d = 75t \]
Here, \(d\) represents distance in miles, \(t\) represents time in hours, and the speed is given as 75 miles per hour.
Domain: The domain typically represents the allowable values for the independent variable, which in this case is time (t). Since time can take on any non-negative value (from 0 to infinity), the domain is:
\[ t \geq 0 \]
Thus, the domain is time (t) and can be represented as \( [0, \infty) \).
Range: The range represents the resulting values for the dependent variable, which here is distance (d). Since distance is calculated as \(d = 75t\) and \(t\) can be any non-negative value, the distance will also be non-negative, meaning:
\[ d \geq 0 \]
Therefore, the range is distance (d) and can also be represented as \( [0, \infty) \).
Considering the options you provided, the correct interpretation is:
The domain is time (t) and the range is distance (d).