1. ## algebra

I have a word problem I cant figure out how they got the answer:

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 1/2 of his time and a 2nd person for 1/3 of her time, WHAT part of the 3rd worker's time should be budgeted to this project?

the answer is 1/6 but I just cant figure how they got that?

Please help. I would really appricate it. I am sure it is simple, but I just cant see it.

2. let x be the amount of time taken for each person to work full time

3rd worker's time = x - (1/2x + 1/3x)
= x - (5/6x)
= 1/6x

3. im stummed!
How do you get

= x - (5/6x)
to
=1/6x

I just am stummed. I feel so stupid. Thanks for you help though.

4. Let's assume that x is full time, it's easy to see that the sums of their times equals x, but each of their times depends on what x is, so:

Time it takes worker 1 = $\frac{1}{2}x$

Time it takes worker 2 = $\frac{1}{3}x$

Time it takes worker 3 = $nx$

Where n is the fraction of full time that the third worker worked, so full time is:

$x = Time_1 + Time_2 + Time_3$

$= \frac{1}{2}x + \frac{1}{3}x + nx$

We want to find n, so we have to solve for n, First, we subtract nx from both sides:

$x - nx = \frac{1}{2}x + \frac{1}{3}x$

Then, we subtract x from both sides:

$-nx = \frac{1}{2}x + \frac{1}{3}x - x$

This is equivalent to the formula in tester's post, now we divide every term on both sides by x:

$-n = \frac{1}{2} + \frac{1}{3} - 1$

Now, we add all the numbers on the right side together using a common denominator of 6:

$-n = \frac{3}{3}\frac{1}{2} + \frac{2}{2}\frac{1}{3} - \frac{6}{6}$

$-n = \frac{3}{6} + \frac{2}{6} - \frac{6}{6}$

$-n = \frac{5}{6} - \frac{6}{6}$

$-n = -\frac{1}{6}$

Now we divide both sides by negative 1 and get:

$n = \frac{1}{6}$

And there you go.

5. From the question itself,

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 1/2 of his time and a 2nd person for 1/3
of her time, WHAT part of the 3rd worker's time should be budgeted to this project?

To better aid in your understanding, Let me repharse the equation based on the question.

their total time on the project is to be equivalent to that of only one person working full time =
1st person work time + 2nd person work time + 3rd person work time

let x be the amount of time taken for each person to work full time

x = (1/2x + 1/3x) + 3rd worker's time
3rd worker's time = x - (1/2x + 1/3x)
= x - (5/6x)
= 1/6x

Hope you can better from the explanation listed above.

Originally Posted by girl in distress
im stummed!
How do you get

= x - (5/6x)
to
=1/6x

I just am stummed. I feel so stupid. Thanks for you help though.