Question

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.

Answer 1

Let the initial speed of the boat be v.
Adding the times for each leg, we get:

`(16)/(v)+(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.