These lessons are compiled to help PreCalculus students learn about rational function problems and applications.

**Related Pages**

Simplifying Rational Expressions

Graphing Rational Functions

PreCalculus Lessons

The following figure shows how to solve rational equations. Scroll down the page for examples and solutions on how to solve rational function problems and applications.

The video explains application problems that use rational equations. Part 1 of 2.

**Examples:**

- Martin can pour a concrete walkway in 6 hours working alone. Victor has more experience and can pour the same walkway in 4 hours working alone. How long will it take both people to pour the concrete walkway working together?
- An inlet pipe can fill a water tank in 12 hours. An outlet pipe can drain the tank in 20 hours. If both pipes are mistakenly left open, how long will it take to fill the tank?

The video explains application problems that use rational equations. Part 2 of 2.

**Examples:**

- One person can complete a task 8 hours sooner than another person. Working together, both people can perform the task in 3 hours. How many hours does it take each person to complete the task working alone?
- The speed of a passenger train is 12 mph faster than the speed of the freight train. The passenger train travels 330 miles in the same time it takes the freight train to travel 270 miles. Find the speed of each train.

Here are a few examples of work problems that are solved with rational equations.

**Examples:**

- Sam can paint a house in 5 hours. Gary can do it in 4 hours. How long will it take the two working together?
- Joy can file 100 claims in 5 hours. Stephen can file 100 claims in 8 hours. If they work together, how long will it take to file 100 claims?
- A water tank is emptied through two drains in 50 minutes. If only the larger drain is used, the tank will empty in 85 minutes. How long would it take to empty if only the smaller drain is used?
- One computer can run a sorting algorithm in 24 minutes. If a second computer is used together with the first, it takes 13 minutes. How long would it take the second computer alone?
- Two pipes are filling a tank. One pipe fills three times as fast as the other. With both pipes working, the tank fills in 84 minutes. How long would each pipe take working alone?

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