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 $T=3/2/3+\sqrt{(3/2{)}^2-6\ast 3/2+13}/2=1/2+\sqrt{1/4+1/2+13}/2=1/2+\sqrt{14.75}/2$.

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 $\boxed{{\displaystyle 3.42}}$ hours.