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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.

Verified Answer :

toporc

Let the initial speed of the boat be v.
Adding the times for each leg, we get:
\(\frac{16}{v}+\frac{12}{v+4}=3\)
This equation results in the following quadratic:
\(3v^{2}-16v-64=0\)
which factorizes to: (3v + 8)(v - 8) = 0
The positive solution is 8.
The answer is 8 mph.

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