SOLUTION: I am trying to figure out how to solve the following math problem: Three people who work full time are to work together on a project, but their total time on the project is to b

Question 1195128: I am trying to figure out how to solve the following math problem:
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-sixth of his time to the project and a second person for one-half of her time, what part of the third worker's time should be budgeted for this project?
1. 1/8
2. 1/3
3. 1/2
4. 3/4
The answer is 1/3. I need to know the steps to arrive at that answer.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let f = full time hours for any one person.
the assumption is that the full time hours for each person is the same.
you get 1/6 * f + 1/2 * f + x = f
1/6 * f is the number of hours for person A.
1/2 * f is the number of hours for person B.
x is the number of hours for person C.
solve for x in the equation to get:
x = f - 1/6 * f - 1/2 * f
put everything under the same denominator to get:
x = f - 1/6 * f - 3/6 * f
solve for x to get:
x = f - 4/6 * f = 2/6 * f
simplify to get:
x = 1/3 * f
that's your answer.
the number of hours for person C is 1/3 * their full time hours.

Answer by MathTherapy(10549) (Show Source): You can put this solution on YOUR website!

I am trying to figure out how to solve the following math problem:
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-sixth of his time to the project and a second person for one-half of her time, what part of the third worker's time should be budgeted for this project?
1. 1/8
2. 1/3
v3. 1/2
4. 3/4
The answer is 1/3. I need to know the steps to arrive at that answer.

You don't have to spend all that time and put all that effort into this like that other person did - it's totally unnecessary. All this involves is: the whole project is one whole or just 1. 1 person is budgeted for of that whole, while the other is budgeted for . This gives us:

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