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A weird walk timing

Source: PRMO 2019 leg 2 P10

August 25, 2019
algebraClocktimePRMO

Problem Statement

One day I went for a walk in the morning at xx minutes past 5′O5'O clock, where xx is a 2 digit number. When I returned, it was yy minutes past 6′O6'O clock, and I noticed that (i) I walked for exactly xx minutes and (ii) yy was a 2 digit number obtained by reversing the digits of xx. How many minutes did I walk?
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