just need a little help
Task 2
John, 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
How do you write the equation in part d?
If the room is the size of a classroom then it might take the friends 9 hours to put all of the coats of paint on that are needed. If it takes 3 friends together to paint the room in 3 hours then it would take each friend alone 9 hours to paint it.
b) If you said they earned $60 per room then they would each get $60 per room.
a. Let's assume that it would take John, Rick, and Molli 6 hours to paint the room together. For John painting the room alone, let's assume it would take him 8 hours, and for Rick painting alone, it would take him 10 hours.
b. To find the hourly rate for John, Rick, and Molli working together, we need to divide the amount of work (1 room) by the time taken (6 hours). So the hourly rate for John, Rick, and Molli when working together is 1/6 rooms per hour.
c. To find the hourly rate for John, we divide the amount of work (1 room) by the time taken (8 hours). So the hourly rate for John is 1/8 rooms per hour.
To find the hourly rate for Rick, we divide the amount of work (1 room) by the time taken (10 hours). So the hourly rate for Rick is 1/10 rooms per hour.
d. The equation comparing the group rate to the sum of the individual rates is:
Group Rate = John's Rate + Rick's Rate + Molli's Rate
Using the values from parts (b) and (c), the equation becomes:
1/6 rooms per hour = 1/8 rooms per hour + 1/10 rooms per hour + Molli's Rate
e. To determine the least common denominator, we take the denominators of the fractions in the equation (6, 8, and 10) and find their least common multiple (LCM). In this case, the LCM of 6, 8, and 10 is 120. So the least common denominator for the equation is 120.
f. To solve the equation and determine how long it will take Molli to paint the room alone, we substitute the values into the equation:
1/6 rooms per hour = 1/8 rooms per hour + 1/10 rooms per hour + Molli's Rate
To get rid of the fractions, we multiply both sides of the equation by the least common denominator (120):
120 * (1/6 rooms per hour) = 120 * (1/8 rooms per hour) + 120 * (1/10 rooms per hour) + 120 * (Molli's Rate)
20 rooms = 15 rooms + 12 rooms + 120 * (Molli's Rate)
20 rooms = 27 rooms + 120 * (Molli's Rate)
To isolate Molli's Rate, we subtract 27 rooms from both sides:
20 rooms - 27 rooms = 120 * (Molli's Rate)
-7 rooms = 120 * (Molli's Rate)
Divide both sides by 120:
-7 rooms / 120 = Molli's Rate
Molli's Rate = -7/120 rooms per hour
Since it doesn't make sense to have a negative rate, we can conclude that Molli's rate cannot be determined based on the given information.
a. To determine a reasonable amount of time, we need to consider the efficiency and skills of John, Rick, and Molli in painting. Let's say it would take them 6 hours to paint the room together.
For John to paint the room alone, let's assume he is more skilled and efficient than the other two, so it would take him 10 hours to complete the task.
Similarly, for Rick to paint the room alone, let's assume he is slightly less skilled than John but more skilled than Molli, so it would take him 12 hours to finish the task on his own.
b. To find the hourly rate for John, Rick, and Molli working together, we divide the total rooms painted by the total time it took them. Let's assume they can paint 1 room in 6 hours together, so their hourly rate would be 1/6 room per hour.
c. The hourly rate for John can be determined by how many rooms he can paint in an hour when working alone. In this case, John can paint 1/10 room per hour. Similarly, the hourly rate for Rick would be 1/12 room per hour.
d. The equation can be written as follows:
Group rate = John's rate + Rick's rate
In terms of rooms per hour:
1/6 = 1/10 + 1/12
e. To determine the least common denominator (LCD) for the equation, we need to find the smallest number that both 10 and 12 can divide evenly. In this case, the LCD would be 60.
f. To solve the equation, we need to eliminate the fractions by multiplying both sides of the equation by 60:
60 * (1/6) = 60 * (1/10) + 60 * (1/12)
10 = 6 + 5
To find Molli's individual rate, we subtract the sum of John and Rick's rates from the group rate:
Molli's rate = Group rate - (John's rate + Rick's rate)
Molli's rate = 1/6 - (1/10 + 1/12)
Molli's rate = 1/6 - 11/60
Molli's rate = 10/60 - 11/60
Molli's rate = -1/60
Since Molli's rate is negative, it indicates that she is not as efficient as John and Rick in painting the room on her own. Therefore, it might not be possible to determine how long it will take Molli to paint the room alone based on the given information.