Activity 3.6.3.
A hiker starting at a point \(P\) on a straight road walks east towards point \(Q\text{,}\) which is on the road and 3 kilometers from point \(P\text{.}\) Two kilometers due north of point \(Q\) is a cabin. The hiker will walk down the road for a while, at a pace of 8 kilometers per hour. At some point \(Z\) between \(P\) and \(Q\text{,}\) the hiker leaves the road and makes a straight line towards the cabin through the woods, hiking at a pace of 3 kph, as pictured in the provided figure. In order to minimize the time to go from \(P\) to \(Z\) to the cabin, where should the hiker turn into the forest?
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