greg drove at a constant speed in a rainstorm for 287 miles. he took a break, and the rain stopped. he then drove 102 miles at a speed that was 10 miles per hour faster than his previous speed. If he drove for 9 hours, find the car's speed for each part of the trip

We first find Greg's average speed as follows. The average speed of a body is defined as the ratio of the total distance travelled by the body to the total time spent.

Total time spent, t = 9 hours

Total distance travelled, s = 287 + 102

s = 389 miles.

Hence the average speed is given thus;

[tex]v_{avg}=\frac{389}{9}\\v_{avg}=43.22mph[/tex]

Let the speed for the first part of his journey be u and that for the last part be v, his average speed can also be expressed as follows;

[tex]v_{avg}=\frac{u+v}{2}...........(1)[/tex]

Hence;

[tex]43.22=\frac{u+v}{2}\\43.22*2=u+v\\86.44=u+v................(2)[/tex]

As stated in the problem, his speed for the final part of the journey was 10mph faster, therefore;

[tex]v=10 +u....................(3)[/tex]

By substituting (3) into (2), we obtain the following;

[tex]86.44=2u+10\\2u=86.44-10\\2u=76.44\\[/tex]

Hence,

[tex]u=\frac{76.44}{2}\\u=38.22mph[/tex]

[tex]v=10+u\\v=10+38.22\\v=48.22mph[/tex]