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  • Send feedback to fisher_d@madera.k12.ca.us Many images from Wikipedia.

Transcript

  • 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