a.
- Reasonable amount of time for John, Rick, and Molli to paint the room together: 2 hours
- Reasonable amount of time for John to paint the room alone: 4 hours
- Reasonable amount of time for Rick to paint the room alone: 3 hours
b.
- Hourly rate for John, Rick, and Molli when working together: 1/2 room per hour
c.
- Hourly rate for John: 1/4 room per hour
- Hourly rate for Rick: 1/3 room per hour
d.
Equation: 1/2 = 1/4 + 1/3
The group rate should be equal to the sum of the individual rates.
e.
The least common denominator for 4 and 3 is 12.
f.
Solving the equation:
1/2 = 1/4 + 1/3
1/2 = 3/12 + 4/12
1/2 = 7/12
Therefore, Molli's hourly rate is 1/12 room per hour. It would take her 12 hours to paint the room alone.
ohn, 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.
3 answers
How would the equation be solved if it were "1/2 < 1/4 + 1/3"?
If the equation is 1/2 < 1/4 + 1/3, we would solve it as follows:
1/2 < 1/4 + 1/3
1/2 < 3/12 + 4/12
1/2 < 7/12
Since 1/2 is less than 7/12, Molli's hourly rate remains at 1/12 room per hour, but in this case, it would take her less than 12 hours to paint the room alone.
1/2 < 1/4 + 1/3
1/2 < 3/12 + 4/12
1/2 < 7/12
Since 1/2 is less than 7/12, Molli's hourly rate remains at 1/12 room per hour, but in this case, it would take her less than 12 hours to paint the room alone.
5 answers