AMC 10 2021-fall-a Problem 4

Mr. Lopez has a choice of two routes to get to work. Route A is $6$ miles long, and his average speed along this route is $30$ miles per hour. Route B is $5$ miles long, and his average speed along this route is $40$ miles per hour, except for a $\frac{1}{2}$-mile stretch in a school zone where his average speed is $20$ miles per hour. By how many minutes is Route B quicker than Route A? $\textbf{(A)}\ 2 \frac{3}{4} \textbf{(B)}\ 3 \frac{3}{4} \textbf{(C)}\ 4 \frac{1}{2} \textbf{(D)}\ 5 \frac{1}{2} \textbf{(E)}\ 6 \frac{3}{4}$