Tom and his brother Harry had a foot race from their home to school, which was an integral number of yards away. Harry ran faster than Tom, but less than twice as fast, and arrived at the school when Tom was still a 2-digit integer of yards behind.

The next day they ran the race again, but this time Harry started farther away from the school by the same amount as the winning margin the previous day, while Tom still started the same time as Harry, but again from home. Of course, since Harry still runs faster, the same ratio as the day before, he finished the difference in distances in less time than it would have taken Tom, but this time the gap at the end was reduced so that when Harry reached school, the amount by which Tom was behind had the two digits reversed from the preceding day.

How far was it from their home to school, and what was their gap at the end of each run when Harry arrived at school?

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