A cyclist is training and has two routes to choose from. Route A is $12$ miles long, and her average speed along this route is $20$ miles per hour. Route B is $10$ miles long, and her average speed along this route is $10$ miles per hour for the first $1$ mile (steep climb), $25$ miles per hour for the next $4$ miles (flat section), and $40$ miles per hour for the remaining distance (downhill). By how many minutes is Route B quicker than Route A?