An adventure race is 9.75 mi long. The race is divided into equal sections. Each section is 0.75 mi long. The race organizer needs 4 volunteers in each section. How many volunteers does the race organizer need? Show your work.
The adventure race has a total distance of \(9.75 \text{ mi}\), and it is segmented into smaller, equal-length sections, each measuring \(0.75 \text{ mi}\). The race organizers require exactly \(4\) volunteers to be stationed in each of these sections. To determine the total number of volunteers needed, we must first find how many sections exist in the race and then multiply that number by the volunteers required per section.
To find the number of sections in the race, we divide the total length of the race by the length of a single section:
\[\text{Number of sections} = \frac{9.75 \text{ mi}}{0.75 \text{ mi}} = 13\]
Thus, the race is divided into \(13\) equal sections.
Since each of the \(13\) sections requires \(4\) volunteers, we multiply the number of sections by the number of volunteers required per section:
\[\text{Total volunteers} = 13 \times 4 = 52\]
Therefore, the race organizer needs a total of \(52\) volunteers.
This method of breaking down a large distance or task into smaller, manageable units is commonly used in event planning and project management. For example, if a company is planning a marathon or a charity walk, they might calculate the total number of water stations or medical staff needed by dividing the total course distance by the interval between stations. This ensures that every part of the route is adequately covered, promoting both safety and efficiency for all participants.