Question

per day and produces 60 electrical components every hour. Find the number of components produced during a working week of 5 days.

Short answer

Answer: The factory produces 2100 electrical components during a working week of 5 days.

Step-by-step solution

Determine the daily production rate

To find the daily production rate, multiply the hourly production rate (60 components per hour) by the number of working hours per day (7 hours). Let the daily production rate be represented by 'D'. D = 7 hours/day * 60 components/hour

Calculate the daily production rate

Now, perform the multiplication to find the daily production rate (D): D = 7 * 60 D = 420 components/day

Determine the weekly production rate

To find the total number of components produced during a working week, multiply the daily production rate (D) by the number of working days in a week (5 days). Let the weekly production rate be represented by 'W'. W = 5 days/week * D components/day

Calculate the weekly production rate

Now, perform the multiplication to find the weekly production rate (W): W = 5 * 420 W = 2100 components/week

Final Answer

The factory produces 2100 electrical components during a working week of 5 days.

Key concepts

Daily Production Rate

Understanding how to calculate the daily production rate is fundamental in various business and manufacturing scenarios. It indicates how much of a particular product a factory, machine, or worker can produce within a single day. In this context, the rate was given as an hourly output which was 60 electrical components per hour. To find the daily total, we simply multiply this rate by the number of productive hours in a day.

For example, let's consider the factory operates for 7 hours a day. The calculation would be:
\[\begin{equation}D = 7 \text{ hours/day} \times 60 \text{ components/hour}d{equation}This results in a daily production of \(D = 420\) components per day. It's essential to understand that this rate can vary depending on several factors including shift lengths, machine efficiency, and workforce productivity. Knowing how to adjust and interpret these figures is key to managing production effectively.

Weekly Production Rate

Once we've established the daily production rate, scaling it to a weekly production rate is the next step. This calculation takes into consideration the number of days worked in the week and can help managers and business owners plan for inventory, manage resources, and meet delivery deadlines.

For the problem at hand, a working week consists of 5 days. Hence, the weekly production rate is a multiplication of the daily production rate by the working days in the week.\[\begin{equation}W = 5 \text{ days/week} \times D \text{ components/day}d{equation}In our case, this would be \(W = 5 \times 420\), resulting in \(W = 2100\) components produced in a week. This figure is crucial for understanding throughput and ensuring a business can meet its output goals regularly.

Mathematical Problem-Solving

Mastering mathematical problem-solving skills is essential for students and professionals alike. It enables one to systematically break down a problem into manageable steps, leading to an effective and efficient solution. In production calculation, the steps usually involve understanding units and conversion, which are critical in minimizing errors.

The approach seen here—identifying rates, calculating daily outcomes, and then extending those to weekly outputs—is a clear example of problem-solving. Breaking the broader question into smaller, sequential steps simplifies the complexity. Additionally, working through this process with clear and concise methodology is beneficial for ensuring accuracy and understanding the implications of the results in real-world scenarios.