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

4. 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

5. 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 hours.

6. 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

7. 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

8. 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

9. 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.