Question

Confused can someone help me thanks. Harold left town driving east at 55 mph. Carol left 2 hours later driving the same route at 65 mph. How many hours after Harold left will it take Carol to catch up to Harold

Answer 1

Harolds position at time time t, H(t) = 55t, make sense?

And Carol's position at time t (for t > 2 hours) is
C(t) = 65(t-2).

So far so good?

Answer 2

yea thanks so much

Answer 3

Now you want to know when Harold's position is equal to Carol's position. That is when Carol catches up. I.e., you want to know the value of t such that
H(t) = C(t)

Answer 4

I am confused now sorry

Answer 5

How far has Harold travelled after t hours?

Answer 6

55m

Answer 7

He's traveling at 55 miles/hour. Hence after t hours, he has travelled a distance of
(55 miles/hour) x (t hours) = 55t miles.

Answer 8

Now Carol. At time t = 2 hours, she leaves. At t = 2 hours exactly, she hasn't travelled anywhere at all. How far has she travelled at t = 3 hours?

Answer 9

http://www.wolframalpha.com/input/?i=55x%3D65%28x-2%29

Answer 10

5 hours after? sorry

Answer 11

Try and follow the logic I'm building up for you. Carol, when she is traveling, travels at a speed of 65 miles/hour. Hence at t = 3 hours, she has been traveling for one hour. How far has she traveled at t = 3 hours?

Answer 12

21

Answer 13

At t = 3 hours, she's been driving for one hour at 65 mph. Hence she has travelled a distance of
distance = speed x time
= 65 miles/hour x 1 hour
= 65 miles
Make sense?

Answer 14

I got 65/2*1 =32.5 did I do it right I am very

Answer 15

sorry to bother u

Answer 16

Let me as you, at time t, for t > 2 hours, how long has Carol been driving?

Answer 17

Do you agree she's been driving (t-2) hours?

Answer 18

yes

Answer 19

Hence at time t, for t > 2, how far has Carol travelled?

Answer 20

=32m 65/2

Answer 21

No. Distance = Speed x Time
Her speed is 65 miles/hour. And the time she's been driving is (t-2) hours. Hence how far has she driven at time t?

Answer 22

130 miles

Answer 23

No. Where did t go?

Answer 24

I am confusing my self with t and miles

Answer 25

Distance = Speed x Time
= 65 miles/hour x (t-2) hours
= 65(t-2) miles

Answer 26

I am so sorry

Answer 27

thanks for all your help I am so sorry to bother u

Answer 28

We're going to finish this. Does that formula for Carol's distance make sense to you?

Distance = Speed x Time
= 65 miles/hour x (t-2) hours
= 65(t-2) miles

Answer 29

no sorry

Answer 30

JamesJ, would it be easier to simplify the problem in to simpler terms that she may understand better?

Answer 31

At time t = 3, how long has Carol been driving?

Answer 32

She seems to be having a hard time grasping the concept of distance traveled over time.

Answer 33

( I don't know how to get away from that. That's the basic concept we're measuring here. )

Answer 34

At time t = 3, how long has Carol been driving?

Answer 35

Or he (sorry I made an assumption with no basis. No offense).

Answer 36

I am a she thanks for helping

Answer 37

I am very sorry to bother I just dont really understand this problem

Answer 38

It's okay. That's what this website is for

Answer 39

Let's try a different approach.

Answer 40

okay

Answer 41

If you are traveling at 65 miles per hour, how far will you have gone in 1 hour?

Answer 42

do I multiply 65 * 60 ?

Answer 43

no

Answer 44

65 miles per hour means you travel 65 miles in 1 (one) hour. In two hours you travel 2*65 miles and so on.

Answer 45

65 miles per hour can also be thought of as 65 miles per 1 hour. So in one hour you will have traveled 65 miles. Does that make sense?

Answer 46

Right Prebz

Answer 47

130 ?

Answer 48

At 65 mph you will have traveled 130 miles in 2 hours does that make sense?

Answer 49

yes

Answer 50

Okay so we know that Harold left two hours before Carol right? He has a 2 hour head start in Carol.

Answer 51

okay

Answer 52

He is going 55 mph so how far has he already traveled when Carol finally gets going?

Answer 53

55*2 will equal 110

Answer 54

Correct.

Answer 55

Now at any point during their travels the time difference between Carol and Harold is going to be the same. Do you agree?

Answer 56

no theres will be different?

Answer 57

How so?

Answer 58

There is no way that Carol can change the time difference without a time machine. She will always into infinity haver left 2 hours after Harold.

Answer 59

yes sorry I was thinking in a different way sorry ur right

Answer 60

Ok so let's call this time difference t-2

Answer 61

So let's look at what that means real quick so, I'm sure you understand.

Answer 62

k

Answer 63

t = the time Harold has driven and t-2 = the time Carol has driven. So when harord has driven for 3 hours how long has Carol driven?

Answer 64

65*3 195?

Answer 65

Harold would have driven 55*3 miles, Carol on the other hand would have driven 65(3-2)miles

Answer 66

no. at this point we are just looking at time only. We will get to distance in a minute.

Since time for Harold is t and time for Carol is t-2 then to figure out how long Carol has driven all you have to do is substitute in how long Harold has driven.

In this case he has driven 3 hours so Carol has driven 3-2 hours.

Does the make sense?

Answer 67

Yes Prebz

Answer 68

yea

Answer 69

Okay cool. So now you understand that time is a constant in this equation and that constant is t-2. Right?

Answer 70

yes

Answer 71

Okay now we can deal with speed and distance which I think you are finally getting the idea of. You know that by the time Carol starts Harold has driven 55*2 miles right?

Answer 72

That is 55 mph * 2 hours.

Answer 73

yes and harold is 110 55*2

Answer 74

Right. Now what we want to know is how long it takes Carol to catch up to Harold. So we can express this as an equation.
55(t)=65(t-2)
Does that makes sense to you?

Answer 75

yes it does

Answer 76

Does it? Where does that equation come from?

Answer 77

Mmm. I think so. Am I mistaken?

Answer 78

It's definitely right. I'm just asking if lala understands where it comes from.

Answer 79

Ah right.

Answer 80

BRB I have to go get my son from school.

Answer 81

okay let me see If I got this right 55(110)=65(130-2) if not I give up so sorry to bother and take up your time thank you for ur patience in teaching me

Answer 82

okay

Answer 83

Ok I'm back.

Answer 84

So my desire to not further confuse you caused me to rush to the equation 55t=65(t-2), but JamesJ was quick to point out that I did not explain how we got there. I don't want to further confuse you, so I'm going to break it down as simply as I know how and if you have further questions you can ask for clarification.

We know that distance traveled (d) is equal to speed (s) multiplied by time (t) or d=st. Since we have two cars traveling, we have two equations:

Harold: d=55t
Carol: d=65(t-2)

Since we are looking for the point where Carol catches up to Harold, we know that the distance is going to be equal in both equations. Therefore:

55t=65(t-2)

And there you go. From here it is just a matter of solving for t, which gives you the amount of time in hours that it will take for Carol to catch up with Harold.

It appears you have left the forum lalaland, so if you have any further questions or need more clarification just respond to this post and I or someone else can explain further until you understand. As I said before, don't worry about trouble us or putting us out. Everyone here is here to help each other, so asking and asking and asking until you understand is not going to put anyone out. As you can see from this thread, if one person is not getting through to you and explaining so that you understand, someone else can step in and try a different way of explaining things.

Answer 85

thank you so much for helping me thank you sorry that I had to go but my internet quit on me. I went back and solved what you had taught me I understand know the problem. Thank you so much again.