smc

Let $r$, $t$, and $d$ represent the rate, time, and distance (respectively) of each trip. We know that $rt=d$, or $r_1{t}_1=r_2{t}_2$. Because it is given that $2r_1=r_2$, $t_1=2t_2$. Furthermore, $d=10t_1=20t_2$. The average speed can be expressed as $\frac{2d}{t_1+t_2}=\frac{2(20t_2)}{2t_2+t_2}=\frac{40}{3}=\boxed{13\frac{1}{3}\text{mph}}$.