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.

Write an equation that represents how many $t$ hours it would take the twins to paint their room working together. Then solve the equation.

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.