41. The road from home to school takes Seryozha 30 minutes. Once on the way, he remembered that he had forgotten a pen at home. Seryozha knew that if he continued on to school at the same speed, he would arrive there 9 minutes before the bell, but if he returned home for the pen, he would, walking at the same speed, be 11 minutes late for the start of the lesson. What part of the way had he walked?
41. Let the distance from home to school be $a$, then the speed is $\frac{a}{30}$. To return home and come back to the place from which he returned, Sergei had to spend 20 minutes $(9+11=20)$. In this time, he would have traveled the distance $\frac{a}{30} \cdot 20=\frac{2}{3} a$. Therefore, Sergei walked from home to the place from which he had to return $\frac{2}{3} a: 2=\frac{a}{3}$, i.e., $\frac{1}{3}$ of the distance.