Grandfather's clock

Algebra Level 4

A grandfather's clock chimes the appropriate number of times to indicate the hour (1 chime for 1 o'clock, 2 - for 2, etc), as well as chiming once at each quarter hour. You are just entering the house, when you hear a single chime. The clock is in a locked room, so you can only hear it, but not see it.

What would be the longest period of time you would have to wait in order to be certain of the correct time (in minutes)?

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