Question

Help 20 POINTS, TOPIC: HOURLY RATES

Amount of Time:
* Three friends can paint the room together – 1 hour
* John can paint the room alone – 4 hours
* Rick can paint the room alone – 5 hours

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.

Answer 1

B.
For all 3 to work together, they can paint 1 room per hour.
C.
John can paint a room at 1/4 of a room per hour.
Rick can paint a room at 1/5 of a room per hour.
Together they can paint a room at a rate of 9/20 of rooms per hour.
D.
1 = 1/4j + 1/5r + 11/20m (john, rick, molli)
E.
The least common denominator is 20
F.
1 = 1/4(0) + 1/5(0) + 11/20x
1 = 0 + 0 + 11/20x
1 = 11/20x
x = 1/(11/20)
x = 1 9/11
It will take Molli 1 hour and 49 minutes (60 x 9/11) to paint the room alone.