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 his 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 into this project?

The problem tells us that the fractions of time worked by the three people need to be equivalent to one person working full time. This means that the fractions need to add up to one. We know one person works one-half (1/2) time on the project and another
works one-third (1/3) time.

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.