chapter 6 section 7 objectives 1 copyright © 2012, 2008, 2004 pearson education, inc. applications...
TRANSCRIPT
Chapter 6 Section 7
Objectives
1
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Applications of Rational Expressions
Solve story problems about numbers.
Solve story problems about distance, rate, and time.
Solve story problems about work.
6.7
2
3
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 1
Solve story problems about numbers.
Slide 6.7-3
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
It is important to check your solution from the words of the problem because the equation may be solved correctly, but set up incorrectly.
Translate:
A certain number is added to the numerator and subtracted from the
denominator of The new number equals the reciprocal of Find
the number.
5.
85
.8
LCD : 5(8 )x
5 8
85 8 5
58
x
xx x
3x
Slide 6.7-4
Solving a Problem about an Unknown NumberCLASSROOM EXAMPLE 1
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 2
Solve story problems about distance, rate, and time.
Slide 6.7-5
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Solve problems about distance, rate, and time.
Recall the following formulas that relate distance, rate, and time.
Slide 6.7-6
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
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.
Solution:
dtr
30
4downtx
10
4upt x
30 10
4 4x x
8x The speed of the boat with no current equals 8 miles per hour.
d r t
Downstream
Upstream
Slide 6.7-7
Solving a Problem about Distance, Rate, and TimeCLASSROOM EXAMPLE 2
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 3
Solve story problems about work.
Slide 6.7-8
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Solve problems about work.
Rate of WorkIf one job can be completed in t units of time, then the rate of work is
1 job per unit of time.rt
Slide 6.7-9
PROBLEM-SOLVING HINTOne job accomplished is equal to the rate of work multiplied by the time worked.
1 jobr t Therefore: 1
r jobt
Making sense: If it takes you 5 hours to do 1 job, you can get of the job done in an hour.
1
5
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
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:
What is Mario’s rate per hour?
What is Al’s rate per hour?
How much time will they work?
How many jobs will they complete?
What is the formula for work?
72 4 or 4 hr
17 17x
1 11
9 8x x
It will take Mario and Al hours if they work together.4
417
Slide 6.7-10
Solving a Problem about Work RatesCLASSROOM EXAMPLE 3