a. Let's say it takes the three friends 3 hours to paint the room together. It would take John 4 hours to paint the room alone and Rick 6 hours to paint the room alone.
b. The hourly rate for the three friends working together is 1/3 room per hour.
c. John's hourly rate is 1/4 room per hour and Rick's hourly rate is 1/6 room per hour.
d. The equation comparing the group rate to the sum of the individual rates is 1/3 = 1/4 + 1/6.
e. The least common denominator for this equation is 12.
f. Solving the equation, we get Molli's rate is 1/12 room per hour. Therefore, it would take Molli 12 hours to paint the room alone.
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.
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