Lesson 4.1  Skills Practice Name_________________________________________________________ Date__________________________

Willie Catchem Analyzing Problem Situations Using Multiple Representations

Problem Set Write an equation that represents the relationship shown in each table. Use the equation to answer the question. 1. Terell is biking around a track. The table show the time it takes Terell to complete several laps around the track. Write an equation that represents the relationship shown in the table. If Terell bikes around the track for 1 hour, how many laps will he complete? Time (minutes)

Distance (laps)

0

0

12

9

24

18

Let t 5 time (minutes) Let d 5 distance (laps) 9 laps speed 5 ​ ___________      ​ 12 minutes © 2011 Carnegie Learning



5 0.75 lap per minute d 5 0.75t

1 hour 5 60 minutes

d 5 0.75t



5 0.75(60)



5 45

If Terell bikes around the track for 1 hour, he will complete 45 laps. Chapter 4      Skills Practice      •      467

Lesson 4.1  Skills Practice

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2. Claudia is jogging around her neighborhood. The table shows the distance Claudia travels during her jog. Write an equation that represents the relationship shown in the table. How long will it take Claudia to jog 5 miles? Distance (miles)

0

0

0.5

1.5

0.75

2.25

© 2011 Carnegie Learning

Time (hours)

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Lesson 4.1  Skills Practice

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Name_________________________________________________________ Date__________________________ 3. Shawna is driving to the beach for summer vacation. The table shows the distance Shawna travels during her trip. Write an equation that represents the relationship shown in the table. How long will it take Claudia to drive the entire 500 mile trip? Distance (miles)

0

0

2

110

3

165

© 2011 Carnegie Learning

Time (hours)

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Lesson 4.1  Skills Practice

page 4

4. Mattie and Lavonne agree to meet and make signs for the pep rally. Lavonne starts 30 minutes early and completes 2 signs before Mattie arrives. The table shows the total number of signs the girls have completed at different times after Mattie arrives. Write an equation that represents the relationship shown in the table. If the girls work for 3 hours after Mattie arrives, what is the total number of signs the girls will complete? Number of Signs

20.5

0

0

2

0.5

4

© 2011 Carnegie Learning

Time (hours)

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Lesson 4.1  Skills Practice

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Name_________________________________________________________ Date__________________________ 5. Juan leaves his home and rides his bike for 15 minutes to the park. After he gets to the park, he resets his odometer to 0 and continues to ride at the same speed. The table shows the distance Juan traveled at the park according to his odometer. Write an equation that represents the relationship shown in the table. If it has been 1.5 hours since Juan left home, what is the distance he rode his bike at the park? Distance (miles)

0.25

0

0.5

1.25

0.75

2.5

© 2011 Carnegie Learning

Time (hours)

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Lesson 4.1  Skills Practice

page 6

6. Lee is a member of the drama club. He is setting up chairs in the gym for the school play. He arrives 5 minutes early and sets up 25 chairs before Jin arrives to help. The table shows the total number of chairs set up at different times after Jin arrives. Write an equation that represents the relationship shown in the table. If Lee and Jin continue at the same pace, how long will it take to set up 300 chairs? Number of Chairs

25

0

0

25

10

75

© 2011 Carnegie Learning

Time (minutes)

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Lesson 4.1  Skills Practice

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Name_________________________________________________________ Date__________________________ Complete each table using the given equation. Use the table to graph the equation. 7. Joelle is ice skating around an ice rink. The equation d 5 0.5t represents the relationship between the time Joelle skates in minutes, t, and the distance she skates in laps, d. Complete the table. Graph the points on the grid. Time (minutes)

Distance (laps)

0

0

10

5

20

10

30

15

50

y

40 30

Distance (laps)

20 10

-50

0 0 -40 -30 -20 -10 -10

x 10

20

30

40

50

© 2011 Carnegie Learning

-20 -30 -40 -50 Time (minutes)

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Lesson 4.1  Skills Practice

page 8

8. Leon is jogging around a park. The equation d 5 5t represents the relationship between the time Leon jogs in hours, t, and the distance he jogs in miles, d. Complete the table. Graph the points on the grid. Time (hours)

Distance (miles)

0 0.25 2.5 1

5

y

4 3

Distance (miles)

2 1 x

0 -2.5 -2.0 -1.5 -1.0 -0.5 -1

0

0.5

1.0

1.5

2.0

2.5

-2 -3

-5 Time (hours)

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© 2011 Carnegie Learning

-4

Lesson 4.1  Skills Practice

page 9

Name_________________________________________________________ Date__________________________ 9. Perry is driving to college. The equation d 5 60t represents the relationship between the time Perry travels in hours, t, and the distance he travels in miles, d. Complete the table. Graph the points on the grid. Time (hours)

Distance (miles)

0 1 2 180

200

y

160 120

Distance (miles)

80 40 x

0 -5

-4

-3

-2

-1 -40

0

1

2

3

4

5

-80

© 2011 Carnegie Learning

-120 -160 -200 Time (hours)

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Lesson 4.1  Skills Practice

page 10

10. Elesha and Jada are making greeting cards to send to the children’s hospital. Jada makes 2 cards before Elesha arrives to help. The equation c 5 2 1 8t represents the relationship between the time Elesha and Jada make cards in hours, t, and the number of cards they make, c. Complete the table. Graph the points on the grid.

Time (hours)

Number of Cards 0

0 0.5 1

10

y

8 6

Number of Cards

4 2 x

0 -2.5 -2.0 -1.5 -1.0 -0.5 -2

0

0.5

1.0

1.5

2.0

2.5

-4 -6

-10 Time (hours)

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Lesson 4.1  Skills Practice

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Name_________________________________________________________ Date__________________________ 11. Ling leaves her home and walks for 15 minutes to the park. After she gets to the park, she resets her pedometer to 0 and continues to walk at the same speed. The equation d 5 2t 2 0.5 represents the relationship between the time Li walks in hours, t, and the distance she walks in the park in miles, d. Complete the table. Graph the points on the grid. Time (hours)

Distance (miles)

0 0 0.5 0.75

2.5

y

2.0 1.5

Distance (miles)

1.0 0.5 x

0 -2.5 -2.0 -1.5 -1.0 -0.5 -0.5

0

0.5

1.0

1.5

2.0

2.5

© 2011 Carnegie Learning

-1.0 -1.5 -2.0 -2.5 Time (hours)

Chapter 4      Skills Practice      •      477