The classes in a school run from 8:15 a.m. until 3:06 P.M. . There are 8 class periods with 5 minutes passing time between classes. How long is each class period?

To solve this scheduling puzzle, the first step is to determine the total length of the school day in minutes. The time from 8:15 a.m. to 3:06 p.m. spans 6 hours and 51 minutes. By converting the hours to minutes (6 hours x 60 minutes) and adding the remaining 51 minutes, we find the entire school day is 411 minutes long. This total duration includes both instructional time and the time students spend moving between classrooms.

The key to this problem is correctly calculating the total passing time. While there are eight classes, there are only seven intervals for passing time between them. Think of it like fence posts; eight posts create seven sections of fence. Therefore, we multiply seven passing periods by five minutes each, which equals 35 minutes of total transit time. Subtracting these 35 minutes from the 411-minute school day leaves us with 376 minutes dedicated purely to classroom instruction.

With the total instructional time calculated, the final step is straightforward. We simply divide the 376 minutes of learning time by the 8 class periods. This calculation reveals that each class period is exactly 47 minutes long. This type of scheduling problem is a practical application of mathematics that school administrators use daily to ensure the school day is structured efficiently, balancing learning time with the necessary logistical breaks for students and staff to move between their classes.