John, Rick, and Molli paint a room together.
Solve the equation below and determine how long it will take Molli to paint the
room alone.
a stack of books in a rectangular prism shaped box.
Let's assume the length of the box is 10 inches, the width is 8 inches, and the height is 6 inches.
Surface Area = 2(10)(8) + 2(8)(6) + 2(10)(6) = 160 + 96 + 120 = 376 sq. in.
Volume = 10 x 8 x 6 = 480 cu. in.
Ratio of Surface Area to Volume = Surface Area/Volume = 376/480 ≈ 0.7833
So, the ratio of surface area to volume for packaging a stack of books in a rectangular box with dimensions 10 x 8 x 6 is approximately 0.7833.
Task 2
A. Reasonable amount of time for all three friends to paint the room together: 5 hours
Reasonable amount of time for John to paint the room alone: 7 hours
Reasonable amount of time for Rick to paint the room alone: 8 hours
B.In order to calculate the hourly rate for John, Rick, and Molli working together, we need to find out how long it takes them to paint the room together and then divide the total number of rooms painted by the total number of hours worked.
Let's say they paint a room in 3 hours when working together.
Total rooms painted: 1
Total hours worked: 3
Therefore, the hourly rate for John, Rick, and Molli working together is:
1 room / 3 hours = 0.33 rooms per hour
So, the hourly rate for John, Rick, and Molli working together is 0.33 rooms per hour.
C.To determine the hourly rates for John and Rick, we first need to determine how long it takes each of them to paint the room alone.
Let's say John can paint the room alone in 5 hours, and Rick can paint the room alone in 4 hours.
This means that together, John and Rick can paint the room in 1 / (1/5 + 1/4) = 20/9 hours.
Therefore, the hourly rate for John would be 1 room / 5 hours = 0.2 rooms per hour.
And the hourly rate for Rick would be 1 room / 4 hours = 0.25 rooms per hour.
D. 0.25 + y - 3 hours + 0.33
0.2
To find the hourly rate for Molli, we can use the following equation:
0.2 (John's hourly rate) + 0.25 (Rick's hourly rate) + y (Molli's hourly rate) = 0.33 (John, Rick, and Molli's combined hourly rate)
0.2 + 0.25 + y = 0.33
0.45 + y = 0.33
y = 0.33 - 0.45
y = -0.12
Molli's hourly rate is -0.12 rooms per hour, which doesn't make sense in this context. It seems like there may have been an error in the calculations leading up to this point.