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The earth rotates 360 degrees in 24 hours, so in one hour it rotates 15 degrees. (If you look at a map of time zones you will see the time zones divided into 15 degree segments). One hour is 60 minutes, so in one minute of time the earth rotates 15/60 degree.
scythian1950 has the right answer. It takes 23 hours 56 minutes and 4 seconds for the Earth to rotate 360 degrees (one sidereal day) and approximately 24 hours to go from noon to noon (one solar day). If it takes 365 1/4 days to orbit the Sun, then the Earth has to rotate nearly 361 degrees to get back to noon. About the only thing I have to add is that 24 hours is the MEAN solar day, or the average amount of time it takes the Earth to rotate from local zenith (noon) to local zenith (noon).