It took Teacher Wang10: 30-10:15 =15 (minutes) to catch up with Teacher Zhang.
Miss Wang10: 45-10: 30 =15 (minutes) to the library.
Available: the distance that the teacher arrives is equal to the distance between the two when Mr. Wang leaves, and Mr. Zhang needs 15 minutes;
Therefore, when Mr. Wang set out, Mr. Zhang had been driving for 15 minutes;
10: 15 forward 15 minutes is 10: 00.
A: Teacher Zhang starts with 10.
So the answer is: 10.