Three people who work full-time are to work together on a project, but their total time on the project is to be equivalent to that of only one person working full-time. If one of the people is budgeted for one-half of this time to the project and a second person for one-third of her time, what part of the third worker's time should be budgeted to this project?
3/6 + 2/6 = ?
Subtract the sum from 6/6
Let's do this step-by-step:
1. Let's first find the common denominator for the fractions representing the time each person is budgeted for. The denominators are 2 and 3, so the common denominator is 2 * 3 = 6.
2. Now, let's calculate the equivalent fractions for each person based on this common denominator:
- The first person is budgeted for 1/2 of their time, which is equivalent to 1/2 * 6/6 = 6/12.
- The second person is budgeted for 1/3 of their time, which is equivalent to 1/3 * 6/6 = 6/18.
3. We know that the total time of these three people working together should be equivalent to one person working full-time, which is 1/1 = 6/6.
4. Therefore, we can subtract the time budgeted for the first two people from the total time to find the time budgeted for the third person:
Total time - (Time budgeted for 1st person + Time budgeted for 2nd person) = Time budgeted for 3rd person
6/6 - (6/12 + 6/18) = Time budgeted for 3rd person
6/6 - (3/6 + 2/6) = Time budgeted for 3rd person
6/6 - 5/6 = Time budgeted for 3rd person
1/6 = Time budgeted for 3rd person
Therefore, the third person should budget 1/6 of their time to this project.
To find the part of the third worker's time that should be budgeted to this project, we need to determine the individual time allocations for each worker first.
Let's assume that the total time required for one full-time person working on the project is represented by "T" (which is equivalent to 1).
The first worker is budgeted for one-half (1/2) of this time, which means they will work for T * (1/2) = 1/2 of their full-time capacity on the project.
The second worker is budgeted for one-third (1/3) of their time, which means they will work for T * (1/3) = 1/3 of their full-time capacity on the project.
Now, to find the remaining time allocation for the third worker, we subtract the time allocated to the first two workers from the total time required for one person:
Remaining time for the third worker = T - (T * (1/2)) - (T * (1/3))
= T - T/2 - T/3
= T * (1 - 1/2 - 1/3)
= T * (6/6 - 3/6 - 2/6)
= T * (1/6)
So, the third worker's time should be budgeted for 1/6 of their full-time capacity to this project.