Hello, Anidem!
Here's another approach to the proboem . . . it takes more baby-talk, though.
If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days,
how long would the job take if Sam, Lisa, and Tom worked together to complete it?
Let \(\displaystyle x\) = number of days for all three to complete the job.
Sam can do the job in 4 days.
In one day, he can do \(\displaystyle \frac{1}{4}\) of the job.
In \(\displaystyle x\) days, he can do \(\displaystyle \frac{x}{4}\) of the job.
Lisa can do the job in 6 days.
In one day, she can do \(\displaystyle \frac{1}{6}\) of the job.
In \(\displaystyle x\) days, she can do \(\displaystyle \frac{x}{6}\) of the job.
Tom can do the job in 2 days.
In one day, he can do \(\displaystyle \frac{1}{2}\) of the job.
In \(\displaystyle x\) days, he can do \(\displaystyle \frac{x}{2}\) of the job.
Together, in \(\displaystyle x\) days. they can do: \(\displaystyle \,\frac{x}{4}\,+\,\frac{x}{6}\,+\,\frac{x}{2}\) of the job.
\(\displaystyle \;\;\)But in \(\displaystyle x\) days, they will complete the entire (1) job.
There is our equation! \(\displaystyle \L\;\;\frac{x}{4}\,+\,\frac{x}{6}\,+\,\frac{x}{2}\:=\:1\)
Solve for \(\displaystyle x\) and get: \(\displaystyle \L\,x\,=\,\frac{12}{11}\,=\,1.0909...\)
