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.
b. What is the hourly rate for John, Rick, and Molli (when working together)? Use rooms per hour as the unit for your rates.
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.
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.
e. What is the least common denominator for the equation you found in part (c)?
f. Solve the equation and determine how long it will take Molli to paint the room alone.
Make a short answer
a.
- Reasonable amount of time for the three friends together: 6 hours
- Reasonable amount of time for John to paint the room alone: 12 hours
- Reasonable amount of time for Rick to paint the room alone: 8 hours
b. The hourly rate for John, Rick, and Molli when working together is 1/6 of a room per hour.
c.
- The hourly rate for John is 1/12 of a room per hour.
- The hourly rate for Rick is 1/8 of a room per hour.
d. The equation comparing the group rate to the sum of the individual rates would be 1/6 = 1/12 + 1/8. The group rate should be equal to the sum of the individual rates when working together.
e. The least common denominator for the equation in part (c) is 24.
f. By solving the equation 1/6 = 1/12 + 1/8, we find that Molli can paint the room alone in 24 hours.