Arithmetic Math

Question

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 of his time to the project 2 and a second person for 1 3 of her time, what part of the third worker’s time should be budgeted to this project?

My tutor says had the two person's budget together and you get 5/6. You subtract 6/6 from 5/6 to get 1/6. My question is how do you get 6/6. Can you please explain this to me in details.

Answer 1

I'm not sure I follow the question fully, but 6/6=1 = one full project

If one worker does 1/2 the project and a 2nd worker does 1/3 of the project, 1/2+1/3=5/6 leaving the remaining 1/6 for the 3rd worker.

To do the full project means doing not a fraction of it, but all of it. All of it means 1 or 6/6 or 12/12 or any ratio where numerator and denominator are equal.

If one worker does 1/2 and another does 1/3, 1/2=3/6 and 1/3 = 2/6 Add them and you get (3+2)/6=5/6

Since the entire project is 1 which equals 6/6, subtract 5/6 from 6/6 getting (6-5)/6 = 1/6.