Theodore is 170 centimeters from the finish line when Alvin crosses it.
The total distance is 451 cm, so we can find the time that takes Alvin to crosses the finish line as follows:
[tex] v_{a} = \frac{x}{t} [/tex] (1)
Where:
[tex] v_{a}[/tex]: is the speed of Alvin = 19.28 cm/s
x: is the total distance = 451 cm
t: is the time that takes Alvin to crosses the finish line =?
By solving equation (1) for t, we have:
[tex]t = \frac{x}{v} = \frac{451 cm}{19.28 cm/s} = 23.4 s[/tex]
Now, after 23.4 seconds have elapsed, Theorode has traveled the following distance ([tex]x_{t}[/tex]):
[tex] x_{t} = v_{t}*t [/tex]
Where:
[tex]v_{t}[/tex]: is the speed of Theodore = 12 cm/s
[tex] x_{t} = v_{t}*t = 12 cm/s*23.4 s = 281 cm [/tex]
The distance (d) that Theodore needs to travel to cross the finish line is:
[tex]d = x - x_{t} = 451 cm - 281 cm = 170 cm[/tex]
Therefore, Theodore is 170 centimeters from the finish line when Alvin crosses it.
You can learn more about speed here: https://brainly.com/question/22610586?referrer=searchResults
I hope it helps you!
