Olivia is staying in a cottage along a beautiful and straight shoreline. A point Q on the shoreline is located 4 kilometers east of the cottage, and an island is located 2 kilometers north of Q (see image
below). Olivia 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 km/hr and swims at a rate of 2 km/hr, what is the minimum possible time it will take Olivia to
reach the island?
You may enter an exact answer or round to the nearest hundredth of an hour.
Island
Water 2 km
Cottage
Q
Shoreline 4 km