1. Chapter 7
Section 7

2. 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

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

4. 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

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

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

7. 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

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

9. 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

10. 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.
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