After sailing 16 mi, a sailor changed direction and increased the boat's speed by 4 mph. An additional 12 mi was sailed at the increased speed. The total sailing time was 3 h. Find the rate of the boat for the first 16 mi.
Let the initial speed of the boat be v. Adding the times for each leg, we get: [tex]\frac{16}{v}+\frac{12}{v+4}=3[/tex] This equation results in the following quadratic: [tex]3v^{2}-16v-64=0[/tex] which factorizes to: (3v + 8)(v - 8) = 0 The positive solution is 8. The answer is 8 mph.
