There are many applications of rational functions. One application uses rationals to determine how much time it will take two people to complete a job if you know how long it will take each one individually.

Emma can paint the fence in her yard in 6 hours. Cora can paint the same fence in 8 hours. How long will it take for them to paint the fence together?

Step 1. Emma can paint 1/6 of the fence in one hour and Cora can paint 1/8 of the fence in one hour.

Let x represent the total time it will take the two girls to paint the fence. Then, use the following equation to help solve this application.


Step 2. Use the rules for adding rational numbers to solve for x.


It will take Emma and Cora 3.43 hours to paint the fence together.