1. Rational Expressions and Equations
Chapter 6
Rational Expressions and Equations

2. Chapter Sections
6.1 – The Domains of Rational Functions and Multiplication and Division of Rational Expressions
6.2 – Addition and Subtraction of Rational Expressions
6.3 – Complex Fractions
6.4 – Solving Rational Equations
6.5 – Rational Equations: Applications and Problem Solving
6.6 – Variation
Chapter 1 Outline

3. Rational Equations: Applications and Problem Solving
§ 6.5
Rational Equations: Applications and Problem Solving

4. Solve Work Problems
To solve work problems we use the fact summarized in the following diagram:
To determine the part of the task done by each person or machine, we use the formula

5. Solve Work Problems
Example After a snowfall, it takes Bud 3 hours to shovel the driveway. It takes Tina 5 hours to shovel the same driveway. If Bud and Tina work together, how long will it take them to shovel the driveway?
Worker
Rate of Work
Time Worked
Part of Task Completed
Bud
1/3 x
x/3
Tina
1/5
x/5
continued

6. Solve Work Problems
WE multiply both sides of the equation by the LCD, 15. Then we solve for x, the number of hours.
continued

7. Solve Work Problems
Answer: Bud and Tina together can shovel the driveway in 15/8 hours, or hours.

8. Solve Number Problems
Number problems involve finding a number related to one or more other numbers.
Example When the reciprocal of 3 times a number is subtracted from 7, the result is the reciprocal of twice the number. Find the number.
Lex x= unknown number. Then 3x is 3 times the number, and 1/3x is the reciprocal of 3 times the number. Twice the number is 2x, and 1/2x is the reciprocal of twice the number.
continued

9. Solve Number Problems
Multiply by the LCD, 6x.

10. Solve Motion Problems
Example Marty and Betty McKane go out on a water bike. When paddling against the current (going out from shore), they average 2 miles per hour. Coming back (going toward shore), paddling with the current, they average 3 miles per hour. If it take ¼ hour longer to paddle out from shore than to paddle back, how far out did they paddle?
continued

11. Solve Motion Problems Bike Distance Rate Time Going out x 2 x/2
Coming back 3
x/5
continued

12. Solve Motion Problems
Therefore, they paddle out 1.5 miles from shore.