3.4 Applied Optimization Activity 3.4.3. A hiker starting at a point P on a straight road walks east towards point Q, which is on the road and 3 kilometers from point P. 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, 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 Figure 3.4.3. In order to minimize the time to go from P to Z to the cabin, where should the hiker turn into the forest? cabin 3 z Figure 3.4.3: A hiker walks from P to Z to the cabin, as pictured.

3.4 Applied Optimization Activity 3.4.3. A hiker starting at a point P on a straight road walks east towards point Q, which is on the road and 3 kilometers from point P. 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, 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 Figure 3.4.3. In order to minimize the time to go from P to Z to the cabin, where should the hiker turn into the forest? cabin 3 z Figure 3.4.3: A hiker walks from P to Z to the cabin, as pictured.