Problem 111 - Introductory and Intermediate Algebra for College Students 4th

Question

An elevator at a construction site has a maximum capacity of 3000 pounds. If the elevator operator weighs 245 pounds and each cement bag weighs 95 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

Step-by-Step Solution

Answer

The elevator can safely lift 28 bags of cement in one trip.

Step 1: Identify the given values

From the problem statement, the maximum weight the elevator can carry is 3000 pounds. The weight of the elevator operator is 245 pounds and the weight of each cement bag is 95 pounds.

Step 2: Calculate the remaining weight limit

Subtract the weight of the operator from the maximum weight limit. The calculation is: \( 3000 - 245 = 2755 \) pounds.

Step 3: Determine the number of cement bags

Divide the remaining weight limit by the weight of a cement bag to find out the maximum number of cement bags that can be lifted. The calculation is: \( 2755 ÷ 95 \).

Step 4: Round down the result

Since we cannot have a fraction of a cement bag, round down the result from step 3 to the nearest whole number.

Key Concepts

Understanding Weight Limits

Weight limits are crucial in ensuring safety, especially in settings like construction sites or warehouses. The weight limit represents the maximum weight a system, machine, or vehicle can safely handle without risking damage or failure. In our context, the elevator at the construction site has a maximum weight capacity of 3000 pounds.

• Weight limits ensure that equipment remains functional and safe for users.
• Exceeding the weight limit can lead to mechanical failure or accidents.
• It is important to consider all weight aspects, including both cargo and operators.

Understanding the weight limits and the reasons behind them is essential for safe operation at any work site.

The Role of Construction Sites

Construction sites are bustling environments where different materials and personnel interact. Each operation must be conducted with safety in mind, especially those involving heavy lifting. Managing resources efficiently is key.

• Elevators are often used in construction to transport heavy materials to different heights safely.
• Adhering to safety protocols such as weight limits ensures that projects run smoothly without unexpected interruptions.
• Planning operations carefully can improve both safety and productivity at these sites.

Effective weight management is vital in maintaining the integrity and progress of construction projects.

Cement Bags as Load

Cement bags are commonly used materials on construction sites. They are often heavy and bulky, making it crucial to calculate their weight accurately when using machinery like elevators.

• Each cement bag in this scenario weighs 95 pounds.
• Operators must calculate how many bags can be loaded based on the remaining weight capacity of the elevator.
• Accurate calculations ensure maximum efficiency without compromising safety.

Understanding how to calculate these loads is an essential skill for construction workers and site managers.

The Division Process in Load Calculation

Division is a mathematical process used to determine how many equal parts fit into a total, which in this context means determining how many bags of cement can fit within the remaining weight capacity. This is done by dividing the available capacity by the weight of each cement bag.

• After accounting for the operator's weight, 2755 pounds are left for cement bags.
• By dividing 2755 by 95, we determine the maximum number of bags that can be transported.
• The division result should be rounded down to the nearest whole number since partial bags cannot be transported.

Mastering division in such practical applications helps ensure that the operations are both efficient and safe.