Renee is staying in a cottage along a beautiful and straight shoreline. A point $Q$ on the shoreline is located 3 kilometers east of the cottage, and an island is located 2 kilometers north of $Q$ (see image below). Renee plans to travel from the cottage to the island by some combination of walking and swimming. She can start to swim at any point $P$ between the cottage and the point $Q$. If she walks at a rate of $3 \mathrm{~km} / \mathrm{hr}$ and swims at a rate of $2 \mathrm{~km} / \mathrm{hr}$, what is the minimum possible time it will take Renee to reach the island?

Enter an exact answer or round to the nearest hundredth of an hour.

Step 1 ：Let's denote the distance from the cottage to the point P where Renee starts swimming as \(x\) (in kilometers). Then the distance from P to Q is \(3 - x\), and the distance from P to the island is the hypotenuse of a right triangle with sides \(3 - x\) and 2, which is \(\sqrt{(3 - x)^2 + 2^2} = \sqrt{x^2 - 6x + 13}\) by the Pythagorean theorem.

Step 2 ：The time it takes Renee to walk from the cottage to P is \(x / 3\) hours, and the time it takes her to swim from P to the island is \(\sqrt{x^2 - 6x + 13} / 2\) hours. So the total time is \(T = x / 3 + \sqrt{x^2 - 6x + 13} / 2\).

Step 3 ：We want to minimize T. To do this, we can take the derivative of T with respect to x, set it equal to zero, and solve for x. The derivative is \(1 / 3 + (x - 3) / (2 \sqrt{x^2 - 6x + 13})\), and setting this equal to zero gives \(x = 3 / 2\).

Step 4 ：Substituting \(x = 3 / 2\) into the expression for T gives \(T = 3 / 2 / 3 + \sqrt{(3 / 2)^2 - 6 * 3 / 2 + 13} / 2 = 1 / 2 + \sqrt{1 / 4 + 1 / 2 + 13} / 2 = 1 / 2 + \sqrt{14.75} / 2\).

Step 5 ：So the minimum possible time it will take Renee to reach the island is approximately \(1.5 + 1.92 = 3.42\) hours. Therefore, the final answer is \(\boxed{3.42}\) hours.