Tourist and distance Puzzle

A tourist wants to go from a to b. there are four ways to do this.
1. to take a wagon. the wagon stops for half an hour at a station in between a & b and then goes to b.
2. to walk to b. if he leavs a at the same time the wagon leaves, he will be between by the wagon by 1 mile to reach b.
3. to walk from a at the same time the wagon leaves from a. he will arrive at the mid station at the time when the wagon is prepared to leave. He can take the wagon from there. this will take shortest time.
4. to go on upto the mid station & to walk from there. he will reach at b 15 minutes before the
wagon. what is the distance between a & b ?.

This question is related to Infosys Interview