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?

Question

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

First, let's calculate the combined rate of John, Rick, and Molli to paint a room together in 4 hours.

Let x be the hourly rate of John, y be the hourly rate of Rick, and z be the hourly rate of Molli.

From the information given, we have the following equations:

1/x = 8
1/y = 6
1/(x+y+z) = 4

Solving the first two equations, we find:
x = 1/8 = 0.125
y = 1/6 = 0.167

Substitute the values of x and y into the third equation:
1/(0.125 + 0.167 + z) = 4
1/(0.292 + z) = 4
0.292 + z = 1/4
z = 1/4 - 0.292
z = 0.008

Therefore, the combined hourly rate of John, Rick, and Molli is $0.125 + $0.167 + $0.008 = $0.30

If they charge $1000 to paint a room, their hourly rate is $1000/4 = $250.

If John charges $950 to paint a room, his hourly rate is $950/8 = $118.75.

If Rick charges $900 to paint a room, his hourly rate is $900/6 = $150.