To calculate the population density, we need to divide the total number of people by the area of the playground.
Step 1: Calculate the total number of people:
Total number of people = number of men + number of women
Total number of people = 80 + 75 = 155
Step 2: Calculate the area of the playground:
Area of the playground = length × width
Area of the playground = 40 meters × 10 meters
Area of the playground = 400 square meters
Step 3: Calculate the population density:
Population density = total number of people / area of the playground
Population density = 155 / 400
Population density = 0.3875 people per square meter
Answer: The population density during the break in the school playground is 0.3875 people per square meter.