Question

Task 2
John, Rick, and Molli paint a room together in 4 hours. John can paint a room alone in 8 hours and Rick can paint a room alone in 6 hours.
If John, Rick, and Molli charge $1000 to paint a room, what is their hourly rate?
If John charges $950 to paint a room, what is his hourly rate?
If Rick charges $900 to paint a room, what is his hourly rate?

Answer 1

Let's denote the hourly rates of John, Rick, and Molli as J, R, and M respectively.

From the given information, we know that John can paint a room alone in 8 hours, Rick can paint a room alone in 6 hours, and together they can paint a room in 4 hours:

John's rate: 1/8 rooms per hour
Rick's rate: 1/6 rooms per hour
(J + R) + M = 1/4 rooms per hour

Since John, Rick, and Molli are together painting a room in 4 hours, their combined rate is 1/4 rooms per hour. We can express this as:

J + R + M = 1/4

Given that their combined rate is 1 room per 4 hours, we can set up the following equation:

1/8 + 1/6 + M = 1/4
Multiplying all terms by 24 to get rid of the fractions:
3 + 4 + 24M = 6
24M = -1
M = -1/24

So, Molli's hourly rate would be -1/24, which does not make sense in the context of painting. This means that the problem is not solvable as given.