After sailing 12 mi, a sailor changed direction and increased the boat's speed by 4 mph. an additional 18 mi was sailed at the increased speed. the total sailing time was 3 h. find the rate of the boat for the first 12 mi.

Let the speed for the first 12 mi be x mi/h, the speed for 18 mi was (x+4) mi/h

thus given that

time=distance/speed

the average time will be:

3 = (12+18) / (x+x+4)

3=30 / (2x+4)

solving for x we get

3 (2x+4) = 30

6x+6=30

6x=24

x=4 mi/hr

Answer: 12 mi/hr