Solving Work Rate Problems: An Example with Computer Assembly

Have you ever encountered a work rate problem that left you puzzled? This article provides a detailed step-by-step solution to a common work rate problem involving men assembling computers. Whether you are a student or an aspiring SEO specialist, this guide will help you understand the underlying concepts and the practical steps involved.

Understanding Work Rate Problems

Work rate problems are prevalent in math and real-life scenarios. Essentially, these problems involve determining the time required to complete a certain amount of work under different conditions. For example, if 10 men can assemble 12 computers in 12 hours, how long will it take 16 men to assemble 24 computers? This article will walk through the solution to this specific problem.

Step-by-Step Solution

Step 1: Determine the Work Rate of the Men

The first step in solving the problem is to calculate the total man-hours required to assemble the given number of computers. Man-hours is a unit of work that represents the amount of work one man can do in one hour. Here's how we can calculate it:

Calculate Total Man-Hours: Number of men 10 Number of hours 12 Total man-hours 10 men × 12 hours 120 man-hours

This total represents the combined effort required to assemble 12 computers.

Step 2: Calculate the Man-Hours per Computer

Next, we need to determine the man-hours required to assemble one computer:

Calculate Man-Hours per Computer: Total man-hours for 12 computers 120 man-hours Man-hours per computer 120 man-hours / 12 computers 10 man-hours per computer

Step 3: Calculate Total Man-Hours Needed for 24 Computers

Now, we need to calculate the total man-hours required to assemble 24 computers:

Calculate Total Man-Hours for 24 Computers: Man-hours per computer 10 man-hours per computer Total man-hours for 24 computers 24 computers × 10 man-hours per computer 240 man-hours

Step 4: Determine the Time It Takes for 16 Men to Assemble 24 Computers

Finally, to find out how many hours it will take for 16 men to complete 240 man-hours of work, we divide the total man-hours by the number of men:

Calculate Time for 16 Men: Total man-hours 240 man-hours Number of men 16 Time 240 man-hours / 16 men 15 hours

Therefore, 16 men will take 15 hours to assemble 24 computers.

Alternative Methods

Another approach to solve this problem is to use the unitary method. This method involves calculating the time required for one man to complete a certain task and then scaling that time to the number of men and tasks involved:

Calculate Time for One Man to Assemble 12 Computers: 10 men take 12 hours to assemble 12 computers, so 1 man would take 120 hours to assemble 12 computers. Calculate Time for One Man to Assemble 24 Computers: Since 1 man takes 120 hours to assemble 12 computers, 24 computers would take 240 hours. Calculate Time for 16 Men: 16 men would take 240 hours / 16 men 15 hours.

Both methods lead to the same conclusion: 16 men will take 15 hours to assemble 24 computers.

Conclusion

This article has provided a comprehensive solution to the work rate problem of assembling computers. The key concepts are the total man-hours required, the man-hours per computer, and the time calculation using both direct and unitary methods. By understanding these steps, you can solve similar work rate problems confidently.

Remember, consistent and proportional work rate is assumed in this problem. In real-world scenarios, other factors such as fatigue, machine efficiency, and task complexity may affect the final time required.

Keywords: work rate, man-hours, assembly problems