3 people work full time together on a project, but their total time on the project is to be equivalent to only 1 person working full time. 1 person worked 1/2 the time, a second person worked 1/3rd of her time. what part of the third workers time should be budgeted for this project

Let x = the amount of time that the third person needs to work on the job to add up to one

1 = 1/2 + 1/3 + x

1 - 1/2 - 1/3 = x

To subtract the fractions we need to put them all over a common denominator. Let's use 3*2 = 6 as the denominator; so 1 = 6/6, 1/2 = 3/6, 1/3 = 2/6:

6/6 - 3/6 - 2/6 = x

1/6 = x

The third person must work 1/6 time on the project.