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Can someone please help me with question d?

John, Rick, and Molli paint a room together.

a. Pick a reasonable amount of time in which the three friends can paint the room together. Also pick a reasonable amount of time in which John can paint the room alone and a reasonable amount of time in which Rick can paint the room alone.

3 hours- 3 friends, 6 hours- John, 8 hours- Rick

b. What is the hourly rate for John, Rick, and Molli (when working together)? Use rooms per hour as the unit for your rates.

The hourly rate for John, Rick, and Molli when working together is; 1/3 of a room per hour.

c. What is the hourly rate for John? What is the hourly rate for Rick? Refer to the
amount of time you determined in which John and Rick can paint the room alone. Use rooms per hour as the unit for your rates.

The hourly rate for John is 1/6 of a room per hour. While, the hourly rate for Rick is 1/8 of a room per hour.

d. Write an equation comparing the group rate to the sum of the individual rates. How should the group rate and the sum of the individual parts compare? Use parts (b) and (c) to help you write the equation.

Respuesta :

       We already know that the hourly rate for John is : 1/6 and the hourly rate for Rick is : 1/8. What we don`t know is a hourly rate for Molly and we will call it 1 / x.
      The hourly rate for all together is: 1 / 3
      An equation is:
      1 / 3 = 1 / x + 1 / 6 + 1 / 8
      1 / 3 = 1 / x + 4 / 24 + 3 / 24
      1 / 3 = 1 / x + 7 / 24
      1 / x = 1 / 3 - 7 / 24
      1 / x = 8 / 24 - 7 / 24
      1 / x = 1 / 24
      1 / 3 = 1 / 24 + 1 / 6 + 1 / 8
      The hourly rate for Molly is 1 / 24. Molly can paint the room alone for 24 hours.

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