Question

Chase and Mikayla are 160 feet apart when they begin walking directly toward one another. Chase travels at a constant speed of 3.5 feet per second and Mikayla travels at a constant speed of 4 feet per second. Let $t$ represent the number of seconds that have elapsed since Chase and Mikayla started walking toward one another. a. Write an expression in terms of $t$ that represents the number of feet Chase has traveled since he started walking toward Mikayla. Preview b. Write an expression in terms of $t$ that represents the number of feet Mikayla has traveled since she started walking toward Chase. Preview c. Write an expression in terms of $t$ that represents the distance between Chase and Mikayla. Preview d. How many seconds after Chase and Mikayla started walking will they reach each other? seconds Preview

          Chase and Mikayla are 160 feet apart when they begin walking directly toward one another. Chase travels at a constant speed of 3.5 feet per second and Mikayla travels at a constant speed of 4 feet per second.
Let $t$ represent the number of seconds that have elapsed since Chase and Mikayla started walking toward one another.
a. Write an expression in terms of $t$ that represents the number of feet Chase has traveled since he started walking toward Mikayla.
Preview
b. Write an expression in terms of $t$ that represents the number of feet Mikayla has traveled since she started walking toward Chase.
Preview
c. Write an expression in terms of $t$ that represents the distance between Chase and Mikayla.
Preview
d. How many seconds after Chase and Mikayla started walking will they reach each other?
seconds Preview
        
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Chase and Mikayla are 160 feet apart when they begin walking directly toward one another. Chase travels at a constant speed of 3.5 feet per second and Mikayla travels at a constant speed of 4 feet per second.
Let t represent the number of seconds that have elapsed since Chase and Mikayla started walking toward one another.
a. Write an expression in terms of t that represents the number of feet Chase has traveled since he started walking toward Mikayla.
Preview
b. Write an expression in terms of t that represents the number of feet Mikayla has traveled since she started walking toward Chase.
Preview
c. Write an expression in terms of t that represents the distance between Chase and Mikayla.
Preview
d. How many seconds after Chase and Mikayla started walking will they reach each other?
seconds Preview

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Chase and Mikayla are 160 feet apart when they begin walking directly toward one another. Chase travels at a constant speed of 3.5 feet per second and Mikayla travels at a constant speed of 4 feet per second. Let t represent the number of seconds that have elapsed since Chase and Mikayla started walking toward one another. a. Write an expression in terms of t that represents the number of feet Chase has traveled since he started walking toward Mikayla. b. Write an expression in terms of t that represents the number of feet Mikayla has traveled since she started walking toward Chase. c. Write an expression in terms of t that represents the distance between Chase and Mikayla. d. How many seconds after Chase and Mikayla started walking will they reach each other?
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Colton and Shannon are 220 feet apart when they begin walking directly toward one another. Colton travels at a constant speed of 3.5 feet per second and Shannon travels at a constant speed of 5 feet per second. Let tt represent the number of seconds that have elapsed since Colton and Shannon started walking toward one another. A. Write an expression in terms of tt that represents the number of feet Colton has traveled since he started walking toward Shannon. B. Write an expression in terms of tt that represents the number of feet Shannon has traveled since she started walking toward Colton. C. Write an expression in terms of tt that represents the distance between Colton and Shannon. D. How many seconds after the two started walking will the reach each other? 2. Jose is 9 feet from a mailbox when all of a sudden he begins walking directly away from the mailbox at a constant speed of 4 feet per second. A. How far is Jose from the mailbox 8 seconds after he started walking? B. Write a formula that expresses Jose's distance from the mailbox (in feet), dd, in terms of the number of seconds tt since he started walking. (Hint: it might help to start with drawing a diagram of the situation.) C. As Jose walks away from the mailbox, is his distance from the mailbox proportional to the time elapsed since he started walking away from the mailbox? I- No, Jose's distance from the mailbox (in feet) is not always the same constant number of times as large as the number of seconds since he started walking. II- No, Jose's distance from the mailbox (in feet) is always larger than the number of seconds elapsed since he started walking. III- Yes, Jose's distance from the mailbox (in feet) is always the same number of times as large as the number of seconds since he started walking. III- Yes, Jose's distance from the mailbox is related to the time elapsed since he started walking.

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Transcript

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00:01 All right, looks like we have a couple of questions here.
00:05 Colton and shannon are 220 feet apart when they begin walking directly toward one another.
00:12 Colton travels at a constant speed of 3 .5 feet per second, and shannon travels at a constant speed of 5 feet per second.
00:22 So we want to let t represent the number of seconds that have elapsed since colton and shannon started walking toward one another.
00:31 Write an expression in terms of t that represents the number of feet.
00:36 Colton has traveled since he started walking towards shannon.
00:43 So let's look at this.
00:44 So we have colton here and we have shannon here.
00:53 And this distance is 220 feet.
01:02 Colton goes 3 .5 feet per second.
01:09 And shannon walks a little bit faster.
01:13 5 feet per second.
01:17 So we want to write an expression in terms of t that represents the number of feet colton has traveled since he started walking toward shannon.
01:27 So for a and b, i've kind of already got it here a little bit.
01:31 So for a, if we want to calculate, so remember t is how many seconds have elapsed since they started walking.
01:44 So for colton, we need to take his speed, 3 .5 .5 .5.
01:51 And so for colton, we need to feet he's going 3 .5 feet per one second and then if we multiply that by t seconds over one this is what is going to give us we're going to get 3 .5 t feet because our units there will cancel just like numbers will and it's very similar for shannon i think this actually is part shannon's going five feet per one second and t seconds over one and we get five t our units there cancel feet so there's part a and part b now we want to write an expression in terms of t that represents the distance between colton and shannon well remember they started out 220 feet apart then we're going to we're going to subtract how many feet colton has traveled, and we're going to subtract how many feet shannon has traveled.
03:10 And that is going to give us the distance.
03:13 We take our initial distance, we subtract how far colton has gone, we subtract how far shannon has gone, and that will give us the distance between the two of them.
03:23 Now, how many seconds after the two started walking will the two reach each other? so what we want to know, we want to solve for t when this distance from part c, the distance between the two of them is equal to zero.
03:44 Because we don't want any distance between them if they're going to reach each other.
03:48 So this is a pretty simple algebraic equation.
03:51 Let me come over here.
03:53 I'm going to have 220 minus 8 .5t.
03:58 That's combining my like terms right here.
04:01 I'm going to subtract, or actually let me add 8 .5t to both sides.
04:11 And so i'm going to get that 220 is equal to 8 .5t.
04:17 And then we divide by this 8 .5 to isolate our t.
04:21 I'm going to have to grab my calculator for that.
04:24 220 divided by 8 .5.
04:27 And i get 25 .88...
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