Math Help - work problem

1. work problem

Hello,
Can someone help explain the method to solve the following problem?

If Sam can do a job in 4 days that Bob can do in 6 days, and Tom can do it in 2 days, then how long would the job take if they all worked together?

I can get get close by using pictures and working through it that way, but I'm looking for the way to set it up in a formula.

BryanC

2. If Sam can do a job in 4 days, he can do 1/4 of the job in a day.
If Bob can do it in 6 days, he can do 1/6 of the job in a day.
If Tom can do it in 2 days, he can do 1/2 of the job in a day.

Together, they can do $\frac{1}{2} + \frac{1}{6} + \frac{1}{4} = \frac{11}{12}$ of the job in a day. If they can do $\frac{11}{12}$ of the job in a day, they can do the job in $\frac{12}{11}$ days.

3. Thanks Wingless... One followup question.

I understand the method to achieve 11/12 of the job in a day. Can you explain how you arrived at 12/11 as the final solution? Thanks Again. I'm sorry for the stupid question.

4. You can achieve it using a simple proportion.

$
\begin{array}{cc}
Day ~~&~~ Job \\ \hline 1 ~~&~~ \frac{11}{12} \\ x ~~&~~ 1
\end{array}
$

In words: If they can do $\frac{11}{12}$ of the job in 1 day, how many days will it take to do the job completely?

$1\cdot1 = \frac{11}{12}\cdot x$

$x = \frac{12}{11}$