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
