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.

The rate of speed of the boat by which sailer sailed the boat for the first 12 miles is 8 miles per hour.
What is the rate of speed?The rate of speed is the rate at which the total distance is travelled in the time taken. Rate of speed can be given as,[tex]r=\dfrac{s}{t}[/tex]Here, s is the distance travelled by the object and t is time taken but the object to cover that distance.Suppose the rate of speed of the boat is r. Thus, the time taken with this speed to clear the 12 miles distance is,[tex]t=\dfrac{12}{r}[/tex]After sailing 12 mi, a sailor changed direction and increased the boat's speed by 4 mph. So the speed become (r+4). With this speed, the time required to cover the additional 18 mi distance is.[tex]t=\dfrac{18}{r+4}[/tex]Total time of both the equation is 3 hours. Thus,[tex]3=\dfrac{12}{r}+\dfrac{18}{r+4}\\3r(r+4)=12r+48+18r\\3r^2+12r=12r+48+18r\\3r^2-48-18r=0\\r^2-6r-16=0\\(x-8)(x+2)=0\\x=8,-2[/tex]Thus, taking positive value of x, the rate of speed of the boat for the first 12 miles is 8 miles per hour. Learn more about the rate of speed here: