Question

Jeff can paint a certain room in 6 hours, but Shawn needs 4 hours to paint the same room. How long does it take them to paint the room if they work together? Construct a rational equation to solve the problem above. Show your work and explain your answer.

Answer 1

1/6 + 1/4 = 1/x

Explanation:

Let x be the time needed for Jeff and Shawn to paint the room working together. Therefore, their rates of work will be as follows:

- Jeff's rate of work: 1 room / 6 hours = 1/6 room per hour

- Shawn's rate of work: 1 room / 4 hours = 1/4 room per hour

When working together, their rates of work are additive, so we have:

- Combined rate of work: 1 room / x hours = (1/6 + 1/4) rooms per hour

Simplifying the equation:

- 1/x = (2/12 + 3/12) / 1

- 1/x = 5/12

Therefore, x = 12/5 = 2.4 hours.

Thus, it takes Jeff and Shawn 2.4 hours to paint the room if they work together.

So, the required rational equation to solve the problem is:

1/6 + 1/4 = 1/x

Where x is the time needed for Jeff and Shawn to paint the room working together.