1. 6.7 Applications of Rational Expressions

2. Objective 1 Solve problems about numbers. Slide 6.7-3

3. It is important to check your solution from the words of the problem because the equation may be solved correctly, but set up incorrectly. Solution: A certain number is added to the numerator and subtracted from the denominator of The new number equals the reciprocal of Find the number. Slide 6.7-4 Solving a Problem about an Unknown Number CLASSROOM EXAMPLE 1

4. Objective 2 Solve problems about distance, rate, and time. Slide 6.7-5

5. Solve problems about distance, rate, and time. Recall the following formulas that relate distance, rate, and time. Slide 6.7-6

6. 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. drt Downstream 30x+4 Upstream 10x−4 Solution: The speed of the boat with no current equals 8 miles per hour. Slide 6.7-7 Solving a Problem about Distance, Rate, and Time CLASSROOM EXAMPLE 2

7. Objective 3 Solve problems about work. Slide 6.7-8

8. Solve problems about work. Rate of Work If a job can be completed in t units of time, then the rate of work is Slide 6.7-9 PROBLEM-SOLVING HINT Recall that the formula d = rt says that distance traveled is equal to rate of travel multiplied by time traveled. Similarly, fractional part of a job accomplished is equal to the rate of work multiplied by the time worked.

9. 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. Slide 6.7-10 Solving a Problem about Work Rates CLASSROOM EXAMPLE 3

10. Solve problems about work. Slide 6.7-11 PROBLEM-SOLVING HINT A common error students make when solving a work problem, like the one in Example 3, is to simply add the two times. In this case, adding Al’s time of 8 hours and Mario’s time of 9 hours together for a total time of 17 hours. This obviously is not a plausible answer since either of the workers alone could complete the project in much less time. Another common error is to try to split the job in half between the two workers so that All would work half of his normal 8 hours and Mario would work half of his normal 9 hours. By doing this, Al would work 4 hours and Mario would work one half hour longer that Al, which would mean that they aren’t actually working together for the last half hour.