Joe can paint a room in 6 hours while Sue can paint the same room in 5 hours. Working together, how long would it take them to paint the room?

A) What does the variable stand for?

x stands for the amount of hours to paint the room.

B)Write the equation.

1/6 + 1/5 = 1/x

c) Solve.

30x [1/6 + 1/5 = 1/x]

5x +6x = 30

11x/11 = 30/1

x = 30/11 or 2.72 hrs.

D) Write the answer in a complete sentence.

It will take Joe and Sue 2.72 hours to paint the room together.

Is this correct?

Yes, your solution is correct. Joe can paint the room in 6 hours, which means he completes 1/6 of the room in one hour. Similarly, Sue can paint the room in 5 hours, so she completes 1/5 of the room in one hour. When they work together, the rate at which they complete the room is the sum of their individual rates, which is 1/6 + 1/5. This is equal to 11/30, which represents the fraction of the room they complete in one hour working together. To find the time it takes to complete the whole room, we can solve the equation 11/30 = 1/x, where x is the number of hours it takes to complete the room. By cross-multiplying and solving for x, we find that x = 30/11 or approximately 2.72 hours. Therefore, it will take Joe and Sue 2.72 hours to paint the room together.

Thanks

The answer is correct but step C should read

(5 + 6)/30 = 1/x

Then x = 30/11