Mo, Merv, and Slope Dude paint a room together. Working all together they can paint the room together in 3 hours. Mo can paint the room alone in 9 hours . Merv can paint the room alone in 6 hours. How long does it take Slope Dude to paint the room alone? A. What is the hourly rate for Mo, Merv and Slope Dude when working together? Use room per hours as the unit for your rates. B. What is the hourly rate for Mo? What is the hourly rate for Merv? What is the hourly rate for Slope Dude using x as the number of hours it takes him to paint the room alone? Use room per hours as the unit for your rates. C. Write an equation comparing the group rate to the sum of the individual rates. Use parts (b) and (c) to help you write the equation. D. What is the least common denominator for the equation you found in part (c)? E. Solve the equation and determine how long it will take Slope Dude to paint the room alone.

Question

Mo, Merv, and Slope Dude paint a room together. Working all together they can paint the room together in 3 hours. Mo can paint the room alone in 9 hours . Merv can paint the room alone in 6 hours. How long does it take Slope Dude to paint the room alone? A. What is the hourly rate for Mo, Merv and Slope Dude when working together? Use room per hours as the unit for your rates. B. What is the hourly rate for Mo? What is the hourly rate for Merv? What is the hourly rate for Slope Dude using x as the number of hours it takes him to paint the room alone? Use room per hours as the unit for your rates. C. Write an equation comparing the group rate to the sum of the individual rates. Use parts (b) and (c) to help you write the equation. D. What is the least common denominator for the equation you found in part (c)? E. Solve the equation and determine how long it will take Slope Dude to paint the room alone.

Answer 1

Let Mo, Merv, and Slope Dude take x,y,z hours, respectively to paint the room. Now we have

1/x + 1/y + 1/z = 1/3
x = 9
y = 6
So z = 18
Now see what you can do with the other questions. Post your work if you get stuck.

Answer 2

To answer these questions, we need to use the concept of "work rates" or "efficiency rates". Work rate is the amount of work done in a unit of time. In this case, we will use "room per hour" as the unit for the work rates.

Let's break it down step by step:

A. The hourly rate for Mo, Merv, and Slope Dude when working together is the sum of their individual rates. To find the individual rates, use the information given.

1. Mo can paint the room alone in 9 hours, so his individual rate is 1 room per 9 hours (1/9).

2. Merv can paint the room alone in 6 hours, so his individual rate is 1 room per 6 hours (1/6).

3. Let's assume Slope Dude takes x hours to paint the room alone. So his individual rate is 1 room per x hours (1/x).

The combined hourly rate for all three working together is given as 1 room per 3 hours (1/3).

B. Now, let's find the individual rates for Mo, Merv, and Slope Dude:

- The hourly rate for Mo is 1/9 (room per hour).
- The hourly rate for Merv is 1/6 (room per hour).
- The hourly rate for Slope Dude is 1/x (room per hour), where x is the number of hours it takes him to paint the room alone.

C. The equation comparing the group rate to the sum of the individual rates can be written as:

1/3 = 1/9 + 1/6 + 1/x

We use the addition of the individual rates because when they work together, their rates add up.

D. The least common denominator for the equation is 18x. Multiply each term by 18x to eliminate the denominators.

18x * (1/3) = 18x * (1/9) + 18x * (1/6) + 18x * (1/x)

6x = 2x + 3x + 18

Simplifying the equation, we get:

6x = 5x + 18

E. Solving the equation:

Subtract 5x from both sides:

6x - 5x = 5x - 5x + 18

x = 18

So, it will take Slope Dude 18 hours to paint the room alone.