Question

Can someone help me answer this Fraction word problem and give step by step how to give the answer?

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 worker's time should be budgeted to this project?

Answer 1

This answer maybe long, but it includes all the essential steps to make it easy
This problem shows that the fraction of the time worked by three individuals need to be = to one person working full time.
It just means that the fractions need to add up to one. Since we got to know that one person works 1/2 the time on the project and the other works 1/3 of the time, let us use a variable to represent the amount of time the last person needs to work to have a total of 1.
This is quite easy:
variable = t(representative of the last person)
step 1: 1=1/2+1/3+t
step 2: keep the variable alone at one side
1-1/2-1/3=t
this step on a calculator will be easy, but dont have a calculator? Thats fine!
Lets have a common denominator
2 and 3 can be 6
1/1*(6/6)-1/2*(3/3)-1/3*(2/2)=t
6/6-3/6-2/6=t
step 3: just subtracts and get the answer
1/6=t
In conclusion, the third person must be working 1/6 the time on the project