An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The total charge flowing through the device is 450 coulombs, which corresponds to approximately 2.81 x 10^21 electrons over 30 seconds.
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Calculate the production rates for factories A, B, C, and D.
Determine the combined production rate of factories A, B, and C.
Calculate the production rates for each table representing factory E.
Identify that all tables could represent the production rate of factory E. All tables could represent the production rate of Factory E.
Explanation
Analyzing Production Rates Let's analyze the production rates of the factories. Factory A produces 600 shirts in 2 days, Factory B produces 900 shirts in 3 days, Factory C produces 1200 shirts in 4 days, and Factory D produces 1500 shirts in 5 days. We need to find the production rates of each factory in shirts per day.
Calculating Individual Production Rates The production rate of Factory A is calculated as: R A = 2 days 600 shirts = 300 shirts/day The production rate of Factory B is calculated as: R B = 3 days 900 shirts = 300 shirts/day The production rate of Factory C is calculated as: R C = 4 days 1200 shirts = 300 shirts/day The production rate of Factory D is calculated as: R D = 5 days 1500 shirts = 300 shirts/day
Determining Combined Production Rate The problem states that Factory D can make shirts at the same rate as the first four factories combined . This means the combined rate of A, B, and C. So, the combined production rate of Factories A, B, and C is: R A BC = R A + R B + R C = 300 + 300 + 300 = 900 shirts/day Since Factory D's rate is equal to this combined rate, we have R D = 900 shirts/day . However, our initial calculation showed R D = 300 shirts/day based on the given data for Factory D alone. This means that the problem statement is slightly ambiguous. We will assume that Factory D's production rate is equal to the combined production rate of Factories A, B, and C, so R D = 900 shirts/day .
Calculating Factory E Production Rates Now, let's calculate the production rates for each of the tables representing Factory E: Table 1: R E 1 = 1 day 400 shirts = 400 shirts/day Table 2: R E 2 = 1 day 300 shirts = 300 shirts/day Table 3: R E 3 = 6 days 1800 shirts = 300 shirts/day Table 4: R E 4 = 6 days 2400 shirts = 400 shirts/day
Identifying Possible Production Rates for Factory E Since the question asks which table(s) could represent the production rate of factory E, any of the tables are valid. The tables represent different possible production rates for Factory E. Therefore, all tables could represent the production rate of Factory E.
Examples
Understanding production rates is crucial in manufacturing and business. For example, if you're managing a factory, knowing the production rate of each machine or worker helps you optimize the production schedule, allocate resources efficiently, and meet customer demands on time. By calculating and comparing production rates, you can identify bottlenecks, improve productivity, and ultimately increase profitability. This concept extends beyond manufacturing to various fields like service industries, project management, and even personal productivity.
