The position on the meter mark where Ari catches up with Amanda is 19.3 m.
The given parameters:
- Range of the number line, = 0 to 30
- Position of the closed circles, = 6 and 25
- The ratio between the initial position and final position of Ari = 7:3
The distance between 6 m mark and 25 m mark is calculated as follows;
[tex]d = 25 \ m - \ 6 \ m\\\\\d = 19 \ m[/tex]
The distance traveled by Ari before catching up with Amanda is calculated as follows;
total ratio = 7 + 3 = 10
[tex]distance = \frac{7}{10} \times 19 \ m\\\\distance = 13.3 \ m[/tex]
The position of Ari from the 6 m mark is calculated as follows;
[tex]position = 6 \ m \ + \ 13.3 \ m\\\\position = 19.3 \ m[/tex]
Thus, the position on the meter mark where Ari catches up with Amanda is 19.3 m.
Learn more about partition of line segments here: https://brainly.com/question/11764811
