Question

The speed of a passenger train is 16mph faster than the speed of a freight train. The passenger train travels 300 miles in the same time it takes the freight train to travel 220 miles. Find the speed of each train.

Answer 1

Call the speed of the freight train x. What's the speed of the passenger train? Using the formula distance = speed * time, how long does it take for the passenger train to go 300 miles? How long does it take for the freight train to go 220 miles? (These will be expressions in x.) Set those expressions equal to each other and solve for x.

Answer 2

Thank you for your response. What I am having a hard time understanding is how to write the equations to get the answer. Can you give an example of one so I can finish off the rest? Thank you.

Answer 3

Try doing the first part of what I wrote. I'll tell you if you get it right or wrong.

Answer 4

300=16*x???

Answer 5

How did you get that?

Answer 6

I think I got it confused with how to write an equation for a problem earlier on in the course. x_x (Anxiety)

Answer 7

Call the speed of the freight train x. What's the speed of the passenger train?

Hint: The answer is in the first sentence of the problem.

Answer 8

300.

Answer 9

300 doesn't appear in the first sentence of the problem.

Explain in your own words what the first sentence says.

Answer 10

16mph. (Oh my, please don't give up on me lol)

Answer 11

I won't give up, as long as you try.
Again, explain in your own words what the first sentence says.

Answer 12

The passenger train is faster than the freight train...

Answer 13

Good. How much faster?

Answer 14

16mph

Answer 15

So, as an example, if the freight train was going 50mph, how fast would the passenger train be going?

Answer 16

66mph?

Answer 17

How did you get that?

Answer 18

I added 16mph to the passenger train because it's faster. (I don't think that's how this is supposed to be solved though.)

Answer 19

If the freight train was going x mph, how fast would the passenger train be going?

Answer 20

300?

Answer 21

How did you get that?

Answer 22

Oops. 16mph?

Answer 23

How did you get that?

Answer 24

I apologize, I am having a hard time understanding this. I am no good at word problems but I will keep trying. D=RT As you stated above. 300=(r+16)T for the passenger train???

Answer 25

How did you get that?

Answer 26

Distance=Rate*Time. So, I think this is the right equation for the passenger train. Is it right?

Answer 27

First tell me how you got it.

Answer 28

Distance is 300. Rate is 16mph * Time but we don't know what time is yet.

Answer 29

Where did the r come from?

Answer 30

I placed the r there for Rate.

Answer 31

Rate of what?

Answer 32

How fast the train was going.

Answer 33

Which train? There are 2.

Answer 34

the passenger train

Answer 35

Why the passenger train?

Answer 36

I think I created that equation first because it was the first train the question mentions. (That probably wasn't a good idea.)

Answer 37

I never said anything was wrong. I just want to know how you got these answers to my questions. I can't help you understand the problem unless I know how you understand it.

Now, in your equation, 300(r+16)t, what does r represent?

Answer 38

Okay. So r represents the rate in the passenger train.

Answer 39

Then how did you get r+16 in the equation?

Answer 40

Hm. I think I meant to write it as a multiplication to multiply rate * time.

Answer 41

Okay, let's go back to my example. If the freight train is going 50mpg, how fast is the passenger train going? The answer is in the first sentence of the question.

Answer 42

The passenger train is going 16mph

Answer 43

Not if the freight train is going 50mph. Again, explain what the first sentence of the problem is telling you.

Answer 44

The passenger train is 16mph faster than the freight train.

Answer 45

Right. So if the freight train is going 50mpg, how fast is the passenger train going?

Answer 46

I am still thinking 66mph and that's where I got the +16 because the passenger train is going 16mph faster than the freight train.

Answer 47

Right. So write a mathematical equation explaining exactly how you got that answer.

Answer 48

The equation is simple. It's just arithmetic.

Answer 49

Your answer was right. It shows the correct thinking. Now you just need to turn it into a mathematical expression.

Answer 50

The equation is simple. It's just arithmetic.

Answer 51

Was that the same mathematical expression I had posted earlier? 300=16/r for the passenger train so for the freight train, I came up with 220=(r+16)t. So 300/r=220/r+16. I got a little extra help from the text book. I believe these are correct since each train can travel for the same length of time.

Answer 52

That's way ahead of where we are right now. Write a mathematical express that shows how you got 66mph as the answer to my question.

Answer 53

Okay. 66=(r+16)t I got to this answer with help from the previous equation.

Answer 54

I said if the freight train is going 50mpg, how fast is the passenger train going? You said "I am still thinking 66mph and that's where I got the +16 because the passenger train is going 16mph faster than the freight train." I want you to write a mathematical expression explaining how you got 66 as the answer to this question.

Answer 55

Okay. 50=(r+16)t

Answer 56

How did you solve the problem I asked?

Answer 57

I added the rate at 16mph to the 50mph freight train.

Answer 58

And what was the answer?

Answer 59

... And the answer was 66.

Answer 60

Right. Now write the mathematical expression you used to solve that problem.

Answer 61

50+16=66.

Answer 62

YES! Now if the freight train is going r mpg, how fast is the passenger train going?

Answer 63

(Do I write a mathematical expression?) The passenger train is going 66mph.

Answer 64

The 50/66 example was just an example to get you to understand what the first sentence is saying. Now I want you to write it as a more general expression, using a variable, r. We're going to call the speed of the freight train r. That way we can write an expression for the speed of the passenger train.

So, using the first sentence, and assuming the speed of the freight train is r, how would you express the speed of the passenger train?

Answer 65

I'm starting to get this a little more, I think. 300=(r+16)t?

Answer 66

You're jumping way ahead. Just look at the first sentence. If we call the speed of the freight train r, what's an expression for the speed of the passenger train?

Answer 67

300=16+r

Answer 68

How did you get that from the first sentence?

Answer 69

300 being from the speed of the passenger train= 16 is distance and r is for the freight train.

Answer 70

The first sentence of the problem doesn't mention 300 or distance.

Answer 71

Please type the first sentence of the problem, word-for-word.

Answer 72

The speed of a passenger train is 16mph faster than the speed of a freight train. So 16+r?

Answer 73

Yes! Do you see how that sentence correlates with that mathematical expression?

Answer 74

I see. :)

Answer 75

So that's where r+16 comes from.

Answer 76

Okay. So now we have the speeds for the two trains: r for the freight train, and r+16 for the passenger train. Let's just work with the passenger train first. Using the formula distance = rate times time (d=rt), write an equation for how far the passenger train goes in time t. You can use data from the second sentence.

Answer 77

t=300/r?

Answer 78

How did you get that?

Answer 79

I got that by using the formula d=rt. However, I do not think this is gonna work. So, 300/r+16? or 300=(r+16)t?

Answer 80

300=(r+16)t is right. But why, exactly?

Answer 81

300 being the speed of the train. r is the rate + 16 * time.

Answer 82

Are you sure?

Answer 83

Scratch the previous answer. The passenger train is going 16mph faster than the freight train. So that is r+16.

Answer 84

Correct. So what's the d=rt equation for the passenger train?
1. What distance does it travel?
2. What's its rate (speed)?
3. How long does it take?

Answer 85

300=(r+16)t. Okay.

Answer 86

Good! Now write an equation for the freight train.

Answer 87

220=(r+16)t.
Distance traveled, rate (speed)* time

Answer 88

Not exactly. What the speed of the freight train?

Answer 89

D'oh! I think that in this case we do, 220/r because we do not have rate for the freight train. So the rate for now is r???

Answer 90

Well, we just assigned the variable r to be the speed of the freight train. The we described the speed of the passenger train in relation to that variable, r. Exactly like the first sentence described.

So, write out the equation for the freight train, just like you did for the passenger train.
1. What distance does it travel?
2. What's its rate (speed)?
3. How long does it take?

Answer 91

220=(r+r)t??

Answer 92

Where did you get r+r?

Answer 93

I got confused. So going back three of your questions. The speed of the freight train is r. 220=(r)t?

Answer 94

Yes.

Now, before we go any further, look back at the first sentence of the problem and remind yourself of how we got r and r+16 for the speeds of the trains. Then look at the d=rt equations you wrote for the two trains, and remind yourself of how we got them from the information in the first two sentences.

Answer 95

This is the gist of story problems. There are several quantities, and they tell you a story about them. Some quantities won't be known, so you'll have to pick variables to assign to them. Some quantities WILL be known (they'll just be numbers). And then they'll give you some ways to relate some of the quantities to some other quantities. You have to write those relationships as mathematical equations, so that you can solve them.

Answer 96

Will do. Does it really matter when you choose any letter as a variable? Or can it be just any to represent that missing number? I took notes of this. I think I'm prepared to answer more on my own for this week's assignment thanks to you.

Answer 97

In this problem, we're dealing with two speeds, two distances, and two times. We can use those to write two d=rt equations. They tell us one speed in terms of the other. They give us explicit values for the distances. And they tell us the times are equal. Once we write the two equations, we have to solve them together. That's the next step.

Answer 98

Okay.