Haun and Wendy are 200 feet apart when they begin walking directly toward one another. Ian travels at a constant speed of 2.5 feet per second and Carolyn travels at a constant speed of 4.5 feet per second.
Let t represent the number of seconds that have elapsed since Ian and Carolyn started walking toward one another.
A) write an expression in terms of t that represent the number of feet Ian has traveled since he started walking toward Carolyn.
B) write an expression in terms of t that represents the number of feet Carolyn has traveled since she started walking toward ian.
C) write an expression in terms of t that represents the distance between Ian and Carolyn.
D) how many seconds after the two started walking will they reach each other?

A) in order to solve this part of the problem, we must remember that velocity is the ratio between a displacement and the time it takes for a body to go from one point to the other. So we can write it like this:

[tex]v=\frac{x}{t}[/tex]

when solvin for the distance x, we get the formula to be:

[tex]x=vt[/tex]

We can use this to write the expression they are asking us for, so we get:

[tex]d_{I}=2.5t[/tex]

B) the procedure for part b is the same as the procedure for par A with the difference that Carolyn's speed is different. So by using the same formula with Carolyn's speed we get:

[tex]d_{C}=4.5t[/tex]

C)

In order to find the distance between Ian and Carolyn, we subtract the distances found on the previous two questions from the 200ft, so we get:

[tex]d=200-d_{I}-d_{c}[/tex]

we can further substitute the d's with the equations we found on the previos two parts of the problem, so we get:

[tex]d=200-2.5t-4.5t[/tex]

which simplififfes to the following:

d=200-7t

D) we can figure the seconds out by substituing the distance for 0 and solving for t, so we get:

0=200-7t

which can be solved for t, lke this:

-7t=-200

[tex]t=\frac{-200}{-7}=28.57[/tex]