Question

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?

Answer 1

Answer:

A) $d_{I}=2.5t$

B)$d_{C}=4.5t$

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:

$v=\frac{x}{t}$

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

$x=vt$

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

$d_{I}=2.5t$

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:

$d_{C}=4.5t$

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:

$d=200-d_{I}-d_{c}$

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

$d=200-2.5t-4.5t$

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

$t=\frac{-200}{-7}=28.57$