Calculating Work Rates and Completion Times: A Seo-Friendly Guide
Introduction
Understanding the relationship between work rates and the completion time of a project is crucial for project managers, PMP aspirants, and anyone involved in project planning. This article explains how to calculate the work rates of individuals and groups, and how to determine the time it takes for them to complete a task together. We will use specific examples to illustrate the steps involved in solving these types of problems.Basic Concepts
Before diving into the problems, it’s important to understand the basic concept of work rates. Work rate is the amount of work an individual or a group can complete in a given unit of time. For example, if 10 boys can complete a job in 10 days, the work rate of one boy is (frac{1}{100}) of the job per day. Similarly, if 20 girls can complete the same job in 10 days, then the work rate of one girl is (frac{1}{200}) of the job per day. Let’s go through these examples in detail.Example 1: 10 Boys or 20 Girls Complete a Job
Suppose 10 boys can complete a job in 10 days. By definition, the total work done is 10 boys times 10 days, which equals 100 boy-days. Similarly, if 20 girls can also complete the job in 10 days, the total work done is 20 girls times 10 days, which equals 200 girl-days. This means 1 boy works in 1 day rate is ( frac{1}{100} ) of the job.
Similarly, for 1 girl in 1 day, the work rate is ( frac{1}{200} ) of the job.
Combined Work Rate: [ text{Combined work rate of 1 boy and 1 girl} frac{1}{100} frac{1}{200} frac{2}{200} frac{1}{200} frac{3}{200} text{ of the job per day} ]
Time to Complete the Job: [ text{Time} frac{1 text{ job}}{text{Combined work rate}} frac{1}{frac{3}{200}} frac{200}{3} approx 66.67 text{ days} ]
Therefore, 1 boy and 1 girl together can complete the job in approximately 66.67 days.
Example 2: 5 Boys and 4 Women Complete a Job
Now, consider another scenario: 5 boys and 4 women can complete a job in 10 days, implying 50 boys and 40 women can complete it in 1 day. Similarly, 5 boys and 3 women can complete the same job in 12 days, so 60 boys and 36 women can complete it in 1 day.
From these statements, we can establish the following relationships:
[ 5W 4W 50B 40W 1 text{ day} ]
[ 5W 3W 60B 36W 1 text{ day} ]
To find the relationship between the work rates:
[ 5/m 4/n 1/10 ] [ 5/m 3/n 1/12 ]
Subtracting the second equation from the first, we get:
[ 4W - 3W 1/3 - 1/10 1/30 ] [ 1/m 1/150 ]
Subtracting the second equation from the first, we get:
[ 1/n 1/10 - 1/12 1/60 ]
Now, using the combined work rate for 1 boy and 2 women:
[ 1/m 2/n 1/T ] [ 1/150 2/60 1/T ] [ 1/150 1/30 1/T ] [ 1/150 5/150 1/T ] [ 6/150 1/T ] [ T 25 text{ days} ]
Therefore, 1 boy and 2 women together can complete the work in 25 days.