1. Applications Work R * T = D Number Situations
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2. 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
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3. Solve problems about numbers.
Objective 1
Solve problems about numbers.
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4. 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.
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5. Solve problems about distance, rate, and time.
Objective 2
Solve problems about distance, rate, and time.
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6. Solve problems about distant rate and time.
Recall the following formulas that relate distance, rate, and time.
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7. 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 sec. What was his rate (to the nearest hundredth of a second)?
(Source:
Solution:
Joey Cheek traveled at a rate of 7.17 meters per second.
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8. 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 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.
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9. 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.
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10. Solve problems about work.
Objective 3
Solve problems about work.
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11. Solve problems about work.
If a job can be completed in t units of time, then the rate of work is
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12. 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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