SOLUTION: Tomas can do a job in 4 hours. Julia can do the same job in 6 hours. How many hours will it take the two of them to do the job if they work together? a. 3.5 b. 2.4 c. 5 d. 2

Heres the way to do it quickly in your head.  Then we'll do it by algebra,
the way your teacher wants you to do it.  But for fun. let's do it the
easy way first:

The least common multiple of 4 hours and 6 hours is 12 hours. If they worked
together for 12 hours Thomas would do 3 jobs and Julia would do 2 jobs.  So
together it would take them 12 hours to do 5 jobs or ths
hours to do one job, which is ths or 2.4 hours. 

By algebra, make this chart:
        
             Number of jobs      Time in hours      Rate in jobs/hour
       
Tomas              
Julia              
Both together      

Let the time for both together be x. and the times for each are
given so fill in all three times:

             Number of jobs      Time in hours      Rate in jobs/hour
       
Tomas                                 4                 
Julia                                 6                 
Both together                         x                 

We are interested in how long it take each and both to do just 1 job,
so we fill in the number of jobs as 1 in each case:


             Number of jobs      Time in hours      Rate in jobs/hour
       
Tomas              1                  4                 
Julia              1                  6                 
Both together      1                  x                 

Next use  to fill in the three
rates:

             Number of jobs      Time in hours      Rate in jobs/hour
       
Tomas              1                  4                 1/4
Julia              1                  6                 1/6
Both together      1                  x                 1/x


To get the equation, use

     Tomas' rate   +    Julia's rate   =   their rate together

          1/4      +        1/6        =         1/x



Multiply through by LCD 12x





hours.


Edwin