Susan and Jack have a painting business. They do not always work in the same location. When working alone, Susan takes 3 hours to paint a room, but Jack takes 2 hours to paint a room the same size. How long would it take to paint the room if they worked together at their usual speeds? Write the equation that represents this problem. Solve and verify your solution

Let t = time Susan and Jack take to paint the room together.

Susan paints rooms per hour.

Jack paints rooms per hour.

Together, they paint rooms per hour.

In this example, negative values of t are called inadmissible values. They are values that are not allowed in the solution because of the conditions given in the word problem.

In this case, the variable t represents time, which cannot be negative. Therefore, the restriction for this rational expression is written as t > 0.

When the solution is substituted into the original equation, the left side of the equation equals the right side of the equation. This means the solution is verified to be correct.