Applications Work R * T = D Number Situations Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Applications of Rational Expressions 7.7 Applications of Rational Expressions 1 Solve problems about numbers. Solve problems about distance, rate, and time. Solve problems about work. 2 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Solve problems about numbers. Objective 1 Solve problems about numbers. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.7 - 3

EXAMPLE 1 Solving a Problem about an Unknown Number A certain number is added to the numerator and subtracted from the denominator of . The number equals the reciprocal of . Find the number. Solution: It is important to check your solution from the words of the problem because the equation may be solved correctly, but set up incorrectly. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.7 - 4

Solve problems about distance, rate, and time. Objective 2 Solve problems about distance, rate, and time. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.7 - 5

Solve problems about distant rate and time. Recall the following formulas that relate distance, rate, and time. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.7 - 6

EXAMPLE 2A Solving a Problem about Distance, Rate, and Time At the 2006 Winter Olympics, Joey Cheek of the United States won the 500-m speed skating event for men in 69.76 sec. What was his rate (to the nearest hundredth of a second)? (Source: http://en.wikipedia.org) Solution: Joey Cheek traveled at a rate of 7.17 meters per second. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.7 - 7

EXAMPLE 2B Solving a Problem about Distance, Rate, and Time In 2004, the Indianapolis 500 race was only 450 mi. Buddy Rice won with a rate of 138.518 mph. What was the time (to the nearest hundredth of an hour)? (Source: World Almanac and Book of Facts 2006) Solution: Buddy Rice’s time was 3.25 hours. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.7 - 8

EXAMPLE 2C Solving a Problem about Distance, Rate, and Time A boat can go 10 mi against a current in the same time it can go 30 mi with the current. The current flows at 4mph. Find the speed of the boat with no current. d r t Downstream 30 x+4 Upstream 10 x−4 Solution: The speed of the boat with no current equals 8 miles per hour. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.7 - 9

Solve problems about work. Objective 3 Solve problems about work. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.7 - 10

Solve problems about work. If a job can be completed in t units of time, then the rate of work is Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.7 - 11

EXAMPLE 3 Solving a Problem about Work Rates Al and Mario operate a small roofing company. Mario can roof an average house alone in 9 hr. Al can roof a house alone in 8 hr. How long will if take them to do the job if they work together? Solution: It will take Mario and Al hours if they work together. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.7 - 12