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Well, if your hour has 60 minutes in it, then

1/2 hour = 30 minutes

1/3 hour = 20 minutes

1/4 hour = 15 minutes

1/5 hour = 12 minutes

1/6 hour = 10 minutes

1/10 hour = 6 minutes

1/12 hour = 5 minutes

1/15 hour = 4 minutes

1/20 hour = 3 minutes

1/30 hour = 2 minutes

But if your hour only has 59 minutes in it, then

1/2 hour = 29.5 minutes or 29 minutes 30seconds

1/3 hour = 192/3 minutes or 19minutes 40seconds

1/4 hour = 14.75 minutes or 14minutes 45seconds

1/5 hour = 11.8 minutes or 11minutes 48seconds

1/6 hour = 95/6 minutes or 9minutes 50seconds

1/10 hour = 5.9 minutes or 5minutes 54seconds

1/12 hour = 411/12 minutes or 4minutes 55seconds

1/15 hour = 314/15 minutes or 3minutes 56seconds

1/20 hour = 2.95 minutes or 2minutes 57seconds

1/30 hour = 129/30 minutes or 1minutes 58seconds

Which choice seems like the more convenient one to you ?

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Q: Why is 60 a good choice for an hour rather than 59?
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