Is this the proper way to set up the equation to answer this question

Here's the question:
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?

Is this how you would set up the equation to solve it?
x/2+x/4+x/6=x

And how would you then solve it? I know I can just plug numbers in but I want the algebraic means of solving it, it's been so long I cant remember. Thanks a lot

Close. Each worker has a rate of work in jobs per day. Since Sam can do a job in 4 days, his rate
is 1/4 jobs/day. Then to figure out how much work he gets done in any given amount of time, you
multply the time by the rate. Working for 1 day, Sam would get (1/4)/(1) = 1/4 job done. If he worked for 8 days get would get (1/4)(8) = 8/4 = 2 jobs done. If you call the time x, then he
gets x/4 jobs done in x days. You've set up the left side of your equation correctly. Since you have 3 people working at rates of x/2, x/4 and x/6. The amount of jobs they can get done in x time is

x/2+x/4+x/6

In this case you only want 1 job done, so you need to solve this equation

x/2+x/4+x/6 = 1

This is done by getting the least common demoninator, which is 12 in this case.

This gets you

6x/12 + 3x/12 + 2x/12 = 1 or

11x/12 = 1 so

x = 12/11 or 1 and 1/11 days

x/2+x/4+x/6=1