Applications

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.

Example
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.

RationalApp1-2

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

RationalApp1-3


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