Chapter 7 Section 7

Applications of Rational Expressions 7.7 Applications of Rational Expressions Solve problems about numbers. Solve problems about distance, rate, and time. Solve problems about work. 2 3

Solve problems about numbers. Objective 1 Solve problems about numbers. Slide 7.7-3

Solving a Problem about an Unknown Number EXAMPLE 1 Solving a Problem about an Unknown Number A certain number is added to the numerator and subtracted from the denominator of The new 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. Slide 7.7-4

Solve problems about distance, rate, and time. Objective 2 Solve problems about distance, rate, and time. Slide 7.7-5

Solve problems about distance, rate, and time. Recall the following formulas that relate distance, rate, and time. Slide 7.7-6

Solving a Problem about Distance, Rate, and Time EXAMPLE 2 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. Slide 7.7-7

Solve problems about work. Objective 3 Solve problems about work. Slide 7.7-8

Solve problems about work. Rate of Work If a job can be completed in t units of time, then the rate of work is 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. Slide 7.7-9

Solving a Problem about Work Rates 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. Slide 7.7-10