The document contains examples of rate of work problems. It shows how to calculate the time it will take two people working together to complete a task by using their individual unit rates. The first example calculates that it will take Marge and Lisa 1 7/8 hours to clean a house if it takes Marge 3 hours and Lisa 5 hours working alone. The second example finds it will take Bart and Homer 12 minutes to wash a car if it takes Bart 20 minutes and Homer 30 minutes alone.

1. Rate of Work Problems by D. Fisher

2. Copyright Notice: All of the images used in this presentation are from the internet and are publicly available. Many of them came from Wikipedia . The content of these presentations are provided by teachers and are presumed to be in the public domain. If any of these materials are used inappropriately, please inform the author , and they will be removed immediately or credit given.

3. Marge can clean the house in 3 hrs. Lisa can clean it in 5 hrs. How long will it take them to clean the house if they both work together?

4. Use Unit Rates Marge can clean the house in 3 hrs., so she does 1 / 3 of the house per hour.

5. Use Unit Rates Lisa can clean the house in 5 hrs., so she does 1 / 5 of the house per hour.

6. Let T be the time in hours. 1 3 T + 1 5 T = 1

7. 1 / 3 T + 1 / 5 T = 1 15( 1 / 3 T + 1 / 5 T) = 15(1) 5T + 3T = 15 8T = 15 T = 15 / 8 1 7 / 8 hrs.

8. Bart can wash the car in 20 min. Homer can wash it in 30 min. How long will it take them to wash the car if they both work together?

9. Use Unit Rates Bart can wash the car in 20 min., so he does 1 / 20 of the car per min.

10. Use Unit Rates Homer can wash the car in 30 min., so he does 1 / 30 of the car per min.

11. Let M be the time in minutes. 1 20 M + 1 30 M = 1

12. 1 / 20 M + 1 / 30 M = 1 60( 1 / 20 M + 1 / 30 M) = 60(1) 3M + 2M = 60 5M = 60 M = 12 min.

13. Springfield School

14. Mr. Skinner can enroll 15 students per hr. Mr. Chalmer can enroll 20 students per hr. How long will it take them to enroll 140 students working together?

15. Use Unit Rates Minutes work better than hours. Mr. Skinner enrolls 15 students per 60 min., so he enrolls 15 / 60 or 1 / 4 students per min.

16. Use Unit Rates Minutes work better than hours. Mr. Chalmer enrolls 20 students per 60 min., so he enrolls 20 / 60 or 1 / 3 students per min.

17. 1 / 4 M + 1 / 3 M = 140 12( 1 / 4 M + 1 / 3 M) = 12(140) 3M + 4M = 1680 7M = 1680 M = 240 min. = 4 hrs.

18. Grading Papers

19. Mrs. Krabappel can grade a set of papers in 1 1 / 2 hrs. Miss Hoover can grade them in 80 min. How long will it take them to grade one set if they both work together?

20. Use Unit Rates Minutes work better than hours. Mrs. Krabappel grades 1 / 90 of a set per min.

21. Use Unit Rates Miss Hoover grades 1 / 80 of a set per min.

22. 1 / 90 M + 1 / 80 M = 1 720( 1 / 90 M + 1 / 80 M) = 720(1) 8M + 9M = 720 17M = 720 M = 42 6 / 17 min.

23. Approximately how long would it take them to grade 3 sets if they both work together?

24. 1 / 90 M + 1 / 80 M = 3 720( 1 / 90 M + 1 / 80 M) = 720(3) 8M + 9M = 2160 17M = 2160 M = 127 1 / 17 min. A little more than 2 hrs.

25. Math Is Fun