In many regions that experience cold temperatures, a simple and working method for dealing with slick roads is covering the ice with sand and/or salt. Towns and cities use trucks to dispense the salt quickly and in bulk. Even though the trucks can hold a large amount of sand in the bed of the truck, fueling and refilling the sand can become an issue of efficiency.
With calculus, we can derive a series of equations to develop a more effective route or method of dispensing. Using equations that relate rates of change to the geometry of the container (ie. change in height, volume, etc.), we are able to find at any time how quickly the sand is being released. With these equations we can determine appropriate timing for refilling, maximizing efficiency of routes given to trucks.