Inductive reasoning

Not too long ago I had to use the inductive reasoning method to figure out a situation. In this situation I was going to school and I was trying to catch up to the bus by driving to the next stop that it was going to make. The distance between these stops is about ten to fifteen miles so it was possible that I would catch up to the bus very quickly. However, I was taking a different road than the one that it first starts out on so I did not see if I had already passed it or if it was in front of me. After driving for a little while I didn't see the bus like I usually do as I pass it. In my head I was trying to figure out what this meant, if the bus had passed me already because on occasion the bus does leave early and this has happened before. On the other hand I could have passed the bus a long time ago not seeing it because we started on different roads. Thinking about it, I decided that the latter would probably be true because I didn't leave that much later than the bus should have and the way I go is faster. As I drive I am looking at the time and it appears that I should be at the stop before the bus but as I see the stop I also see the bus leaving, it did leave early and I did miss it, I was wrong. 
Premiss one: the bus had left early and it was far ahead of me. 
Premiss two: I beat the bus by going the faster way at first and I was far ahead of it.
 Conclusion: I must be in front of the bus beaches I took the faster way in the beginning. 
In the end I was wrong and that resulted in me going slower not going faster to catch the bus.