Twelve Hour Period

In a twelve-hour period of time, for how many minutes is the number of the hour greater than the number of the minute?
Source: NCTM Mathematics Teacher

SOLUTION

From 12\!:\!00 to 12\!:\!12,12 minutes
From 11\!:\!00 to 11\!:\!11,11 minutes
From 10\!:\!00 to 10\!:\!10,10 minutes
etc.
From 3\!:\!00 to 3\!:\!03,3 minutes
From 2\!:\!00 to 2\!:\!02,2 minutes
From 1\!:\!00 to 1\!:\!01,1 minute
Total minutes
1+2+3+\cdots+11+12=\frac{\left (1+12\right )12}{2}
=\frac{\left (13\right )12}{2}
=13\times 6
=78

Answer: 78 minutes

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About mvtrinh

Retired high school math teacher.
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