Two ways:

First way:  In your head

The LCM of their times, 45 minutes and 30 minutes, is 90 minutes
So in 90 minutes Frank does 2 jobs, while Erika does 3 jobs.
So together they can do 2+3 or 5 jobs in 90 minutes
So they can do 1 job in 1/5 of 90 or 18 minutes. 

Second way.  By algebra:

Make this chart with x for the time for both to do 1 job.
Put in the times for the two workers to do the job separately
and put 1 for the number of jobs:

       number of jobs    time in minutes   rate in jobs/minute
Frank         1                45
Erika         1                30
Both          1                 x

Now fill in the column on the right by dividing number of jobs 
by the number of minutes

       number of jobs    time in minutes   rate in jobs/minute
Frank         1                45                 1/45
Erika         1                30                 1/30
Both          1                 x                 1/x

To get the equation:

           Frank's rate + Edith's rate = The combined rate for both
                 1/45   +    1/30      =       1/x

Clear of fractions by multiplying through by 90x

                               2x + 3x = 90    
                                    5x = 90
                                     x = 18

Edwin