Expert: Steve Holleran - 2/21/2007

Question
carminia can hand embroider a table cloth in 9 days while jennifer can do it in 12 days. in how many days, can they finish a rush order if they work together?

Answer
Hello Can,

You can solve many of these "work" problems using the same method we're going to go through here.

Lets make x the number of days it takes them to do the job working together.

If Carminia does the job in 9 days, then in 1 day she will do 1/9 of the job, and then in x days she will do x/9 of the job.

Likewise, if Jennifer does the job in 12 days, then in 1 day she'll do 1/12 of the job and in x days she will do
x/12 of the job.

Our equation becomes :

  Part done by Carminia + Part done by Jen = 1 job

          x/9           +       x/12       = 1

Now multiply both sides by 36, the LCD of 9 and 12:

           4x            +        3x        = 36

                                  7x         = 36

so x = 36/7 = 5 1/7 days.

I hope this helps you out.
Good luck.

Steve Holleran