Fraction Problem

[jjamesdk]

Hi everyone. I need some help understanding this 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-half of his time to the project and
a second person for one-third of her time, what part of the
third worker’s time should be budgeted to this project?

I find that just multiplying 1/2 and 1/3 will give me the answer of 1/6, which is the correct answer, but I don't understand why this gives me the correct answer. Can anyone show me the appropriate steps (algorithm) to use to solve the problem?

Will be much appreciated, thanks

 

[lookagain]

Hi everyone. > > > I need some help understanding this 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-half of his time to the project and
a second person for one-third of her time, what part of the
third worker’s time should be budgeted to this project?

I find that just multiplying 1/2 and 1/3 will give me the answer of 1/6, which is the correct answer,
but I don't understand why this gives me the correct answer. Can anyone show me the appropriate
steps (algorithm) to use to solve the problem?

I need some help understanding this problem, too.

In a nutshell, it sounds as if the first person does 1/2 of the time on the project, and
the second person does 1/3 of the time on the project. And then it appears to ask
how much of the remaining time on the project that the third person does.

*If* that is the case, then the remaining fraction of time could be worked out be adding
the two fractions together and subtracting them from 1 (which represents 100% of the time).

That is, \(\displaystyle \ \ 1 \ - \ (\frac{1}{2} \ + \ \frac{1}{3}) \ \ = \ \ \) the fraction of the time for the third person.

The fact that the product of 1/2 and 1/3 equals 1/6 is a mere coincidence in this problem.


First, 1/2 + 1/3 = what?

 

[jjamesdk]

It works!

I need some help understanding this problem, too.

In a nutshell, it sounds as if the first person does 1/2 of the time on the project, and
the second person does 1/3 of the time on the project. And then it appears to ask
how much of the remaining time on the project that the third person does.

*If* that is the case, then the remaining fraction of time could be worked out be adding
the two fractions together and subtracting them from 1 (which represents 100% of the time).

That is, \(\displaystyle \ \ 1 \ - \ (\frac{1}{2} \ + \ \frac{1}{3}) \ \ = \ \ \) the fraction of the time for the third person.

The fact that the product of 1/2 and 1/3 equals 1/6 is a mere coincidence in this problem.


First, 1/2 + 1/3 = what?

After trying your method of deducing down the problem it worked!, 1/2 + 1/3 = 5/6, and subtracting that from 1/1 or ( 6/6 ) in this case gave me 1/6. I'm still curious though if there is another way to solve it, though it is simple enough , thank you so much!