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This problem trains for: SAT-I, AMC-8, AMC-10, GMAT, Math Kangaroo 5-6, Math Kangaroo 7-8, Math Kangaroo 9-10.

A machine stops automatically for 8 minutes after every half hour of operation, in order to cool down. After the first 6 hours of the day, approximately what percentage of the time has been spent in operation?

The time is divided into units of 38 minutes each: 30 minutes of operation plus 8 minutes of cooling time. The total time in minutes is 360 minutes (6 hours). Integer division gives us the number of 38 minute intervals and the time remaining after the last break:

There are 9 intervals, therefore 9 breaks. The total number of minutes spent in breaks is:

The total number of minutes spent operating is:

The percentage of time spent in operation x, is 80% of the total time: