Rational Expressions and Equations

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Presentation transcript:

Rational Expressions and Equations Chapter 6 Rational Expressions and Equations

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

6.5: Rational Equations: Applications and Problem Solving 1. Solve Work problems. 2. Solve Number problems. 3. Solve Motion problems.

Solve Work Problems Example 1: 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 Time of Work Rate of Work Bud 3 Tina 5 1/3 1/5 Together x 1/x

Example 1: Second method Worker Rate of Work Time Worked Part of Task Completed Bud 1/3 x x/3 Tina 1/5 x/5 Answer: Bud and Tina together can shovel the driveway in 15/8 hours, or 1.875 hours.

Example 2: Louis and Rebecca own a painting business. Louis can paint an average size room in 2 hours. Rebecca can paint the same room in 7 hours. How long would it take them to paint the same room working together? Worker Time of Work Rate of Work Louis 2 1/2 Rebecca 7 1/7 Together x 1/x

Solve Number Problems Example 3: When the reciprocal of 3 times a number is subtracted from 7, the result is the reciprocal of twice the number. Find the number. Let the number be x

Solve Motion Problems Example 4: A sports car travels 15 mph faster than a loaded truck on the freeway. In the same time that the sports car travels 156 miles, the truck travels 120 miles. Find the speed of each vehicle. Use a table to organize the information. Vehicle Distance Rate Time Sports car Truck 156 miles r + 15 120 miles r

Solve Motion Problems Therefore, they paddle out 1.5 miles from shore. Example 5: A couple of friends 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? Water Biking Distance Rate Time Against the current: Going out With the current: Coming back x 2 x / 2 x 3 x / 3 Therefore, they paddle out 1.5 miles from shore.