A cyclist rode on a paved trail and a gravel path to complete a $30$-mile ride. The ride took $3$ hours. The cyclist's average speed was $12$ mph on the paved trail and $6$ mph on the gravel path. If $p$ is the time, in hours, the cyclist spent on the paved trail and $g$ is the time, in hours, the cyclist spent on the gravel path, which system of equations represents this situation?