Question

\"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 and a second is budgeted for one-third her time, what portion of the third worker's time should be budgeted to this project?\":

Solve the problem without using a calculator. Show your solution.

Answer 1

Third person is budgeted for one-sixth of his time.

Explanation:

Let x be the third worker's time that should be budgeted to this project.

It is given that three people who work full-time are to work together on a project.

First worker's time that should be budgeted =
`(1)/(2)`

Second worker's time that should be budgeted =
`(1)/(3)`

It is given that total time on the project is to be equivalent to that of only one person working full-time, i.e. 1.

`(1)/(2)+(1)/(3)+x=1`

Isolate the variable x.

`x=1-(1)/(2)-(1)/(3)`

Taking LCM, we get

`x=(6-3-2)/(6)`

`x=(1)/(6)`

The value of x is 1/6. Therefore the third person is budgeted for one-sixth of his time.

Answer 2

the equation to be used here is 1 full shift = 1/2 shift + 1/3 shift +x shift
equating everything to x you get x = 1 - 1/2 - 1/3 = 1/6