Rick, John, and Molli are painting a room.
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.
a. Reasonable amount of time for the three friends to paint the room together: 4 hours
Reasonable amount of time for John to paint the room alone: 6 hours
Reasonable amount of time for Rick to paint the room alone: 8 hours
b. Hourly rate for John, Rick, and Molli (working together): 1/4 room per hour
c. Hourly rate for John: 1/6 room per hour
Hourly rate for Rick: 1/8 room per hour
d. Equation comparing the group rate to the sum of the individual rates:
Group rate (1/4) = Rate of John (1/6) + Rate of Rick (1/8)
Can you show the "d." step with just the equation, please?
Sure! Here is the equation comparing the group rate to the sum of the individual rates:
Group rate = Rate of John + Rate of Rick
1/4 = 1/6 + 1/8