When the Hobbits needed to know the time of day they looked at the sun and guessed.
They had no need for acurate time measuring.
There were no religeous services to be observed at particular times. That need led to the developement of clocks in our own Middle Ages. There were no trains running to a timetable, the thing that led to the standarisation of time across nations in our Nineteeth Century. They had no science that needed precise timing for research.
Hobbits didn't worry about time. The got up when the sun rose, they ate when they were hungry, they went to sleep when they were tired and they were content.
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