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 determine the length of each instructional block, we first calculate the total duration of the school day. From 8:15 a.m. to 3:06 p.m., the total time elapsed is 6 hours and 51 minutes. This breaks down into 3 hours and 45 minutes until noon, plus another 3 hours and 6 minutes after noon. Converting this total into minutes gives us 6 multiplied by 60, plus 51, which equals 360 + 51, or 411 minutes in total.

Next, we account for the time spent transitioning between lessons. With 8 distinct class periods, there are 7 intervals of passing time between them. Each break lasts 5 minutes, so the total time dedicated to moving through hallways is 7 multiplied by 5, resulting in 35 minutes. Subtracting this transition time from the overall school day duration leaves us with the actual instructional time: 411 minutes minus 35 minutes, which equals 376 minutes devoted solely to learning.

Finally, to find the duration of a single class period, we divide the total instructional time by the number of classes. Dividing 376 minutes by 8 class periods yields exactly 47 minutes per period. This kind of precise scheduling is crucial for schools, balancing academic instruction with necessary breaks and logistics. From the ringing of the first bell to the final dismissal, every minute of the school day is carefully allocated to maximize learning opportunities and ensure a smooth flow, a testament to the practical application of basic arithmetic in everyday life.