 # Applications of Rational Expressions

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How to solve word problems that involve rational expressions?

Applications of Rational Expressions
Example:
The speed of a plane is seven times as great as the speed of a car. The car takes 3h longer than the plane to travel 315 km. Determine the speed of the car and the speed of the plane, in km/h.
Rational Equations: Applications - Work Word Problems
Here are a few examples of work problems that are solved with rational equations.
1. Sam can paint a house in 5 hours. Gary can do it in 4 hours. How long will it take the two working together?
2. 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?
3. 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?
4. 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?
5. 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 will each pipe take working alone?

Direct variation application | Rational expressions | Algebra II
Example:
In outer space the distance an object travels varies directly with the amount of time that it travels. If an asteroid travels 3000 miles in 6 hours what is the constant of variation?
Inverse variation application | Rational expressions
Example:
On a string instrument the length of a string varies inversely as the frequency of its vibrations (the vibrations are what give string instruments their sound). An 11-inch string has a frequency of 400 cycles per second. Find the constant of proportionality and then find the frequency of a 10-inch string.

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