Respuesta :
Answer:
38.22mph and 48.22mph
Explanation:
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]
