There are 3 people who work full-time and 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 1/2 of his time to the project and a second person for 1/3 of her time, what part of the third workers time should be budgeted to this project ?

The problem express that the fraction of time worked by the three people need to be equivalent to one person working full time. This means that the fraction need to add up to one. We know one person works ½ time on the project and another works one third 1/3 time.

Given:

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

1 = ½ +1/3 + A

1 – ½ - 1/3 = A

To subtract the fractions put them all over a common denominator. Use 3 * 2 as the denominator.

1=6/6, ½ = 3/6, 1/3 = 2/6

A = 6/6 – 3/6 – 2/6

A = 1/6 , The third person  must work on the project

the answer to the expression is 83