Evelyn 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). Evelyn 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 7 km/hr and swims at a rate of 2 km/hr, what is
the minimum possible time it will take Evelyn to reach the
island?
You may enter an exact answer or round to the nearest hundredth
of an hour.