Objective - To solve rational equations.Solve. x 2

x 1 x 1

Variable in denominator

Restriction: x 1

x(x 1) 2(x 1)2x x 2x 2

2x 2x 2x 3x 2

2 2 2x 3x 2 0

(x )(x ) 0 1 2

x 1 or x 2 However, x 1

2x

Solve.

3 1 5

x 2 x Variable in denominator

Restriction: x 0

3 1 5

x 2 x

6 x 106 6

x 4

Solve.

2

2 x1

x 2 x 2x

Variable in denominator

Restriction: x 22 x1

x 2 x(x 2)

or x 02 x

x(x 2) 1x 2 x(x 2)

2x x x(x 2) 2x x 2x 20 x x

x x

0 x(x 1) x 0 or x 1

Objective - To solve chart problems involving work.

Work Rate Time Work Done

Work Rate Time Work Done

5 hrs. 1 Job1 Job5 hrs.

or 15

Job / hr.

Jeff can paint a room in 4 hours. It takesHal 5 hours to paint the same room. How long will it take them if they work together?

Work Rate Time Work Done Jeff

Hal

1415

x

x

14

x

15

x

114

15

1x x

2014

15

1x x FH IK

Jeff can paint a room in 4 hours. It takesHal 5 hours to paint the same room. How long will it take them if they work together?

Work Rate Time Work Done Jeff

Hal

1415

x

x

14

x

15

x

1

5 4 20x x 9 20x x

209

229

hrs.

One water hose can fill a pool in 10 hours.A different hose only takes 6 hours. How long would it take if both hoses are used?

Work Rate Time Work Done 10 hr. hose6 hr. hose

11016

x

x

110

x

16

x

1110

16

1x x

301

1016

1x x FH IK

Work Rate Time Work Done

1

3 5 30x x 8 30x x

308

334

hrs.

10 hr. hose6 hr. hose

11016

x

x

110

x

16

x

One water hose can fill a pool in 10 hours.A different hose only takes 6 hours. How long would it take if both hoses are used?

John can tile a 10’ x 10’ room in 80 minutes.It takes Sam 2 hours. If John works alone for 30 minutes and then Sam helps him finish, howmuch longer will the job take?

Work Rate Time Work Done John

Sam

1801

120

x 30

x

180

30x a f1

120x

1180

301

1201x x a f

2401

8030

1120

1x x FH IKa f

John can tile a 10’ x 10’ room in 80 minutes.It takes Sam 2 hours. If John works alone for 30 minutes and then Sam helps him finish, howmuch longer will the job take?

Work Rate Time Work Done John

Sam

1801

120

x 30

x

180

30x a f1

120x

1

3 30 2 240x x a f x 30 min.

Julie can complete a wedding cake in 8 hours.Marty can put one together in 10 hours. If Julie and Marty work together for 4 hours, how long will it take Julie to finish the job alone?

Work Rate Time Work Done Julie

Marty

181

10

4 x

4

18

4 xa f4

1011

84

410

1 xa f

4018

44

101 FH IKxa f

Work Rate Time Work Done

1

Julie

Marty

181

10

4 x

4

18

4 xa f4

10

5 4 16 40( ) x x 45

hr. 48 min.

Julie can complete a wedding cake in 8 hours.Marty can put one together in 10 hours. If Julie and Marty work together for 4 hours, how long will it take Julie to finish the job alone?

Mixture Problem #1A 12 pound mixture of peanuts and cashews sellsfor $6.50/lb. If peanuts sell for $3 per pound and cashews sell for $8 per pound, how many pounds of peanuts are in the mix?

# pounds Price/lb. Total Price Peanuts

Cashews

Mixture

12

38

6.5

x

12 x3x

8(12 x)78

3x 8(12 x) 78 3.6 lbs. peanuts & 8.4 lbs. cashewsx 3.6

Mixture Problem #2A 10% acid solution is mixed with a 60% acidsolution to produce 120 liters of a solution thatis 40% acid. How much of each solution was used to create the mixture?

Solution % Acid Total Acid 10% Sol.

60% Sol.

40% Mix

120

0.100.60

0.40

x

120 x0.10x

0.60(120 x)48

0.10x 0.60(120 x) 48 x 16

16 L 10% Sol. &104 L 60% Sol.