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)

B)

C) d=200-7t

D) t=28.57s

Step-by-step explanation:

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:

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

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

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:

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:

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

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