In order to solve problems involving working together, it is necessary to
The goal of a “working together” problem is generally to figure how fast a job can be completed if two or more workers complete the job together.
Suppose that it takes Janet 6 hours to paint her room if she works alone and it takes Carol 4 hours to paint the same room if she works alone. How long will it take them to paint the room if they work together?
First, we will let x be the amount of time it takes to paint the room (in hours) if the two work together.
Janet would need 6 hours if she did the entire job by herself, so her working
rate is
of the job in an hour. Likewise, Carol’s
rate is
of the job in an hour.
In
x hours, Janet paints
of the room and Carol paints
of the room. Since the two females will be working together, we will add the two parts together. The sum equals
one complete job and gives us the following equation:
We are now ready to solve this
equation to determine how long it will take the two females to paint the room if they work together.



Multiply each term of the equation by the common denominator 12 

Simplify 

Collect like terms 
hours 
Solve for x 
Remember that
x represents the amount of time it takes to paint the room (in hours) if the two work together. So, working together, the two females can paint the room in only
hours or 2 hours and 24 minutes.