Step 1 :Jesse can paint a room in 3 hours and her twin can paint a room in 4 hours. They want to work together to repaint their room over the weekend.
Step 2 :The rate at which Jesse can paint a room is 1 room per 3 hours, or \(\frac{1}{3}\) of a room per hour. Similarly, the rate at which her twin can paint a room is 1 room per 4 hours, or \(\frac{1}{4}\) of a room per hour.
Step 3 :When they work together, their rates of painting add up. So, the combined rate at which they can paint a room is \(\frac{1}{3} + \frac{1}{4} = \frac{7}{12}\) of a room per hour.
Step 4 :To find out how long it would take them to paint the room together, we can set up the equation \(\frac{7}{12} * t = 1\), where t is the time in hours it takes for them to paint the room together.
Step 5 :Solving this equation for t will give us the answer.
Step 6 :The solution to the equation is approximately 1.714, which means it would take the twins approximately 1.714 hours to paint the room together.
Step 7 :Final Answer: The twins would take approximately \(\boxed{1.714}\) hours to paint the room together.