2. Rational Expressions and Functions
Chapter 8
Rational Expressions and Functions

3. Applications of Rational Expressions
8.5
Applications of Rational Expressions

4. 8.5 Applications of Rational Expressions
Objectives
Find the value of an unknown variable in a formula.
Solve a formula for a specified variable.
Solve applications using proportions.
Solve applications about distance, rate, and time.
Solve applications about work rates.
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5. 8.5 Applications of Rational Expressions
Find the Value of an Unknown Variable in a Formula
Current
Total resistance
In electronics, the formula for calculating the total resistance r of parallel resistors r1 and r2 is given by the formula
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6. 8.5 Applications of Rational Expressions
Find the Value of an Unknown Variable in a Formula
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7. 8.5 Applications of Rational Expressions
Solve a Formula for a Specified Variable
To solve for a variable means to isolate that variable on one side of the equal sign.
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8. 8.5 Applications of Rational Expressions
Solve a Formula for a Specified Variable
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9. 8.5 Applications of Rational Expressions
Solve Applications Using Proportions
Ratios enable us to compare numerical quantities.
A certain chainsaw requires that the gasoline be mixed with oil in the ratio of 32 to 1.
In the stock market, winning stocks might outnumber losing stocks in the ratio of 7 to 3.
The ratio of a to b may be written in any of the following ways:
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10. 8.5 Applications of Rational Expressions
Solve Applications Using Proportions
A proportion is a statement that two ratios are equal.
Examples of proportions:
Proportions are a useful and important type of rational equation.
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11. 8.5 Applications of Rational Expressions
Solve Applications Using Proportions
A toy model indicates on the box that 1 inch on the model is equivalent to 18 inches on the actual automobile. How long will the model be if the actual automobile is feet long?
1 inch : 18 inches x
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12. 8.5 Applications of Rational Expressions
Solve Applications Using Proportions
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13. 8.5 Applications of Rational Expressions
Solve a Proportion Problem Involving Rates
Alicia spent 5 hours studying for her last accounting exam and got 60% on the exam. She has already studied 2 hours for her upcoming second exam and would like to get 90% on that exam. If we assume that Alicia continues to increase her score at the same rate as before, how much more should she study to get 90%?
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14. 8.5 Applications of Rational Expressions
Solve a Proportion Problem Involving Rates
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15. 8.5 Applications of Rational Expressions
Applications Involving Distance, Rate, and Time
The current of a river is 3 miles/hour. It takes a motorboat a total of 3 hours to travel 12 miles upstream and return 12 miles downstream. What is the speed of the boat in still water?
Solution
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16. 8.5 Applications of Rational Expressions
Applications Involving Distance, Rate, and Time
Total time is 3 hours.
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17. 8.5 Applications of Rational Expressions
Applications Involving Distance, Rate, and Time
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18. 8.5 Applications of Rational Expressions
Applications Involving Distance, Rate, and Time
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19. 8.5 Applications of Rational Expressions
Applications About Work Rates
Work problems are closely related to time, rate, and distance problems.
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20. 8.5 Applications of Rational Expressions
Applications About Work Rates
An inlet pipe can fill a backyard pool in 10 hours, while the drain can empty it in 12 hours. If both the inlet pipe and the drain are open, how long will it take to fill the pool?
10 hours to fill pool
12 hours to empty pool
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21. 8.5 Applications of Rational Expressions
Applications About Work Rates
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22. 8.5 Applications of Rational Expressions
Applications About Work Rates
Copyright © 2010 Pearson Education, Inc. All rights reserved.

23. 8.5 Applications of Rational Expressions
Applications About Work Rates
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