Task 2
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.
a. Reasonable amount of time:
- Together: 4 hours
- John alone: 6 hours
- Rick alone: 8 hours
b. Hourly rate for John, Rick, and Molli (working together):
- Together: 1/4 room per hour
- John: 1/6 room per hour
- Rick: 1/8 room per hour
c. Hourly rate for John and Rick:
- John: 1/6 room per hour
- Rick: 1/8 room per hour
d. Equation comparing group rate to sum of individual rates:
1/4 = 1/6 + 1/8
e. Least common denominator: 24
f. Solving the equation:
1/4 = 4/24 (group rate)
1/6 = 4/24 (John's rate)
1/8 = 3/24 (Rick's rate)
4/24 = 4/24 + 3/24
4/24 = 7/24
Molli's rate = 1 - (7/24) = 17/24 or approximately 0.708 rooms per hour
So, it will take Molli approximately 24/17 = 1.41 hours to paint the room alone.