The Mad Hatter's Watch

Stage: 3 Short Challenge Level: Challenge Level:1

The hour hand on the Mad Hatter's watch moves at the correct speed, but the minute hand moves one and a half times as fast as it should. Yesterday, it showed the correct time at 3 p.m. When did it next show the correct time?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.
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