Reasonable amount of time for the three friends to paint the room together: 6 hours
Reasonable amount of time for John to paint the room alone: 9 hours
Reasonable amount of time for Rick to paint the room alone: 8 hours
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.
5 answers
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
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 for the three friends to paint the room together: 4 hours
Reasonable amount of time for John to paint the room alone: 8 hours
Reasonable amount of time for Rick to paint the room alone: 6 hours
b. Hourly rate for John, Rick, and Molli when working together: 1/4 room per hour
(The three friends can paint the room in 4 hours, so they complete 1 room in 4 hours, hence 1/4 room per hour).
c. Hourly rate for John: 1/8 room per hour
Hourly rate for Rick: 1/6 room per hour
d. Equation comparing the group rate to the sum of the individual rates:
1/4 = 1/8 + 1/6
The group rate should be equal to the sum of the individual rates.
e. The least common denominator for the equation 1/8 and 1/6 is 24.
f. Solving the equation:
1/4 = 1/8 + 1/6
6/24 = 3/24 + 4/24
6/24 = 7/24
Therefore, it will take Molli 24/7 = 3.43 hours to paint the room alone.
Reasonable amount of time for John to paint the room alone: 8 hours
Reasonable amount of time for Rick to paint the room alone: 6 hours
b. Hourly rate for John, Rick, and Molli when working together: 1/4 room per hour
(The three friends can paint the room in 4 hours, so they complete 1 room in 4 hours, hence 1/4 room per hour).
c. Hourly rate for John: 1/8 room per hour
Hourly rate for Rick: 1/6 room per hour
d. Equation comparing the group rate to the sum of the individual rates:
1/4 = 1/8 + 1/6
The group rate should be equal to the sum of the individual rates.
e. The least common denominator for the equation 1/8 and 1/6 is 24.
f. Solving the equation:
1/4 = 1/8 + 1/6
6/24 = 3/24 + 4/24
6/24 = 7/24
Therefore, it will take Molli 24/7 = 3.43 hours to paint the room alone.
Suppose you are having a birthday party at the local bowling alley. You are trying
to figure out how many people you can afford to invite.
a. The number of guests you can invite to your party varies inversely with the
price per bowler at the alley. Explain what this means.
b. How much money are you willing to spend to host this bowling party?
c. Set up an equation that shows the inverse relationship between the number
of guests at your party and the price per bowler. Your answer to part (b)
should be part of this equation.
d. Research two local bowling alleys. Record the price per bowler at each of
these two alleys.
Calculate how many guests you will be able to invite to your party at each of the
bowling alleys. Which alley would you choose for your party? Why?
to figure out how many people you can afford to invite.
a. The number of guests you can invite to your party varies inversely with the
price per bowler at the alley. Explain what this means.
b. How much money are you willing to spend to host this bowling party?
c. Set up an equation that shows the inverse relationship between the number
of guests at your party and the price per bowler. Your answer to part (b)
should be part of this equation.
d. Research two local bowling alleys. Record the price per bowler at each of
these two alleys.
Calculate how many guests you will be able to invite to your party at each of the
bowling alleys. Which alley would you choose for your party? Why?
a. The statement "The number of guests you can invite to your party varies inversely with the price per bowler at the alley" means that as the price per bowler increases, the number of guests you can invite decreases, and vice versa. This is because the total cost you are willing to spend on the party remains constant.
b. Let's say you are willing to spend $200 to host the bowling party.
c. Let x be the number of guests you can invite to the party, and y be the price per bowler. The equation representing the inverse relationship between the number of guests and the price per bowler is:
x = k/y
where k is a constant value (in this case, $200).
d. Let's assume Alley A charges $10 per bowler and Alley B charges $15 per bowler.
For Alley A:
x = 200/10 = 20 guests
For Alley B:
x = 200/15 ≈ 13.33 guests (rounding down to 13 guests)
You would choose Alley A for your party because it allows you to invite more guests (20 guests) compared to Alley B (13 guests) within your budget of $200.
b. Let's say you are willing to spend $200 to host the bowling party.
c. Let x be the number of guests you can invite to the party, and y be the price per bowler. The equation representing the inverse relationship between the number of guests and the price per bowler is:
x = k/y
where k is a constant value (in this case, $200).
d. Let's assume Alley A charges $10 per bowler and Alley B charges $15 per bowler.
For Alley A:
x = 200/10 = 20 guests
For Alley B:
x = 200/15 ≈ 13.33 guests (rounding down to 13 guests)
You would choose Alley A for your party because it allows you to invite more guests (20 guests) compared to Alley B (13 guests) within your budget of $200.