When working together, Bart and Lisa can clean their entire house in 2 hours. Working alone, Bart can clean the house in 5 hours. How long would it take Lisa to clean the house by herself? (express your answer in hours and minutes)

#1#1

#2#2 #3#3Simplify Simplify

4 389

5 7

1 12 3

#4#4 Simplify

2

6 x2x

1 1 15 x 2

When working together, Bart and Lisa can clean their entire house in 2 hours. Working alone, Bart can clean the house in 5 hours. How long would it take Lisa to clean the house by herself? (express your answer in hours and minutes)

#1#1

Time Work Rate

Bart

Lisa

Tog

5

x

2

1

5

1

x

1

2

1 1 15 x 2

2x 10 5x

10 3x

10

3 hours = 3

1

3 hours

10

x3

3 hrs.,20 min.3 hrs.,20 min.

When working together, Bart and Lisa can clean their entire house in 2 hours. Working alone, Bart can clean the house in 5 hours. How long would it take Lisa to clean the house by herself? (express your answer in hours and minutes)

#1#1

#2#2 Simplify

32

Complex Fractions

4 389

4 83 9

4 9

3 8

2 2 3 33 2 2 2

32 2 33 2 2 2

#3#3 Simplify Complex Fractions

5 7

1 12 3

5 756

5 67 5

67

5

73

62

6 =5

7⋅6

5

#4#4 Simplify

3x

Complex Fractions

2 3 xx x 2

2

6 x2x

2

6 x2x

3

x2 x

x 2

Rational ExpressionsRational ExpressionsChapter 10Chapter 10

Rational ExpressionsRational ExpressionsChapter 10Chapter 10

Word ProblemsWord Problems

Motion Problems

Work Rate

MixtureSolution

Mixture ProblemsMixture Problems

50 Liter50 Liter 20 Liter20 Liter 30 Liter30 Liter

AcidAcid WaterWater

Mixture ProblemsMixture Problems

QQQQ TTTTWWWWHHHH

50 Liter50 Liter 20 Liter20 Liter 30 Liter30 Liter

AcidAcid WaterWater

Mixture ProblemsMixture Problems

QQQQ TTTTWWWWHHHH

50 Liter50 Liter 20 Liter20 Liter 30 Liter30 Liter

40%40%Acid solutionAcid solution

40%40%Acid solutionAcid solution

AcidAcid WaterWater

Mixture ProblemsMixture Problems

QQQQ TTTTWWWWHHHH

50 Liter50 Liter 20 Liter20 Liter 30 Liter30 Liter

40%40%Acid solutionAcid solution

40%40%Acid solutionAcid solution

AcidAcid WaterWater40%40%Acid solutionAcid solution

40%40%Acid solutionAcid solution

40%40%Acid solutionAcid solution

40%40%Acid solutionAcid solution

Mixture ProblemsMixture Problems

QQQQ TTTTWWWWHHHH

50 Liter50 Liter 20 Liter20 Liter 30 Liter30 Liter

AcidAcid WaterWater40%40%Acid solutionAcid solution

40%40%Acid solutionAcid solution

40%40%Acid solutionAcid solution

40%40%Acid solutionAcid solution

0.4 20 0.4 30

8 12

Original

New

Krissy has 8 gallons of fruit punch for a party. The punch is Krissy has 8 gallons of fruit punch for a party. The punch is 25% orange juice and the rest of it is apple juice. She wants 25% orange juice and the rest of it is apple juice. She wants to make a drink that consists of 40% orange juice. How many to make a drink that consists of 40% orange juice. How many gallons of orange juice must she add to the existing mixture?gallons of orange juice must she add to the existing mixture?

O.J.Total

mixture

2 8

x = amount of orange juice must be added?

2 x 8 x

2 x0.40

8 x

2 x 28 x 5

10 5x 16 2x

3x 6x 2

#1#1

2 gallons of O.J . 2 gallons of O.J .

Original

New

A doctor has 500 ml of a solution that is half alcohol. She A doctor has 500 ml of a solution that is half alcohol. She needs a solution that is 60% alcohol. How many ml of alcohol needs a solution that is 60% alcohol. How many ml of alcohol should she add?should she add?

AlcoholTotal

Solution

250 500

x = amount of alcohol to be added.

250 x 500 x

250 x0.60

500 x

250 x 3500 x 5

1250 5x 1500 3x

2x 250

x 125

#2#2

Original

New

Ignacio, a world renowned chemist has 400 mL of a cleaning Ignacio, a world renowned chemist has 400 mL of a cleaning solution that is 20% bleach. He wants to make a solution solution that is 20% bleach. He wants to make a solution that is 50% bleach. How much bleach should he add to the that is 50% bleach. How much bleach should he add to the solution?solution?

Bleach Totalmixture

80 400

x = amount of bleach that must be added.

80 x 400 x

80 x0.5

400 x

#3#3

160 2x 400 x

80 x 1

400 x 2

x 240

#1#1 Paige, the famous Hollywood beautician to the stars, has Paige, the famous Hollywood beautician to the stars, has 400 mL of a hair dying solution that is 30% bleach. She 400 mL of a hair dying solution that is 30% bleach. She wants to make a solution that is 60% bleach. How many mL wants to make a solution that is 60% bleach. How many mL of bleach should she add to the solution?of bleach should she add to the solution?

Nicholas owns a motorcycle that goes 12 mph faster than Nicholas owns a motorcycle that goes 12 mph faster than his friend Matthew’s moped. The two left on a trip to a his friend Matthew’s moped. The two left on a trip to a cabin in the mountains 217 miles away. When Nate arrived cabin in the mountains 217 miles away. When Nate arrived at the cabin Brady still had 42 miles to go. Find the speed at the cabin Brady still had 42 miles to go. Find the speed of Nicholas’ motorcycle. of Nicholas’ motorcycle.

Haley can type a 20 page paper in 5 hours. Abhina can type Haley can type a 20 page paper in 5 hours. Abhina can type a 60 page paper in 8 hours. Working together, how long a 60 page paper in 8 hours. Working together, how long would it take them to complete a 40 page paper? (round would it take them to complete a 40 page paper? (round your answer to the nearest minute)your answer to the nearest minute)

#2#2

#3#3

#4#4

Bailey, the fabulous chef at Chez Dennez, has prepared 20 Bailey, the fabulous chef at Chez Dennez, has prepared 20 quarts of soup. Bailey was horrified to find out that she quarts of soup. Bailey was horrified to find out that she made a mistake in the recipe and the soup that she made a mistake in the recipe and the soup that she prepared is only 10% chicken stock. Bailey needs to make prepared is only 10% chicken stock. Bailey needs to make the soup with 20% chicken stock. How much pure chicken the soup with 20% chicken stock. How much pure chicken stock should she add to the original soup?stock should she add to the original soup?