Two problems: linear distance and directed graph

[jangoom]

1.) Two volumes of an encyclopedia stand side by side, in order, on a shelf. A bookworm starts at page i of Volume I and bores its way in a straight line to the last page of Volume II. Each cover is 1 mm thick, and the first volume is
2/5 as thick as the second volume. The first volume is 40 mm thick without its cover. How far does the bookworm travel?

2.) Heres the 2nd question in the attacthments, as it may require a picture to show you...

A car pulls into the USS Nimitz, which is now a car ferry. As the car enters the ferry, there are four rows of traffic directors arranged in a triangular pattern, such that one director is in the first row, two are in the second, three are in the third, and four are in the fourth row. They are directing traffic into five parking spots, as shown below.

Given that cars must proceed according to traffic arrows, how many different paths are there into each of the parking spots?
Paths to A:

Paths to B:

Paths to C:

Paths to D:

Paths to E: If its the wrong section, forgive me but I don't know what kind of math this is..

I don't need just the answer, I want to know how you do the problem to get the answer as well so I am able to answer it next time it comes up in my class. Much thanks to whoever answers me...

 

[Greg]

Hi jangoom and welcome to MHB! :D

I've edited the title of your post to accurately reflect the nature of the problems given. Also, we ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

 

[jangoom]

Thanks for replying greg. Uhhh the thing is I haven't done math in years and I don't even know how to start. I just started an online math class, and homework was given, but my book hasn't arrived and there's no way for me to do the homework without the book and this homework is due in 2 days. I need the answer as well as how to do it.. thanks.

 

[I like Serena]

Thanks for replying greg. Uhhh the thing is I haven't done math in years and I don't even know how to start. I just started an online math class, and homework was given, but my book hasn't arrived and there's no way for me to do the homework without the book and this homework is due in 2 days. I need the answer as well as how to do it.. thanks.

Hey jangoom! ;)

That's quite an unreasonable pressure to you - due in 2 days!
Still, if we can't tell where you're stuck, we'll just be giving either too basic or too advanced help.
Please, just give us a clue of what you do or don't understand and/or how it is that you don't know how to begin!

 

[jangoom]

Well, uh that's kinda the point I'm trying to make.. I have absolutely no idea how to go about these problems..

Maybe you could give me a formula to work with and we can go from there? Your replies are encouraging.. thanks.

 

[I like Serena]

Well, uh that's kinda the point I'm trying to make.. I have absolutely no idea how to go about these problems..

Maybe you could give me a formula to work with and we can go from there? Your replies are encouraging.. thanks.

Okay...

1.) Two volumes of an encyclopedia stand side by side, in order, on a shelf. A bookworm starts at page i of Volume I and bores its way in a straight line to the last page of Volume II. Each cover is 1 mm thick, and the first volume is
2/5 as thick as the second volume. The first volume is 40 mm thick without its cover. How far does the bookworm travel?

So let's see... if we put a volume on a shelf, I think its front page is typically on the right side, and the the last page is on the left side, isn't it?
If the bookworm starts on page i, I think it starts on the right side, on the left of the cover, and bores to the right through the cover, right? (Wondering)
So how far would it travel to the right before hitting the last page of volume ii?

 

[jangoom]

... I really don't know. Like I've sat hwee for at least 2 hrs hoping someone could help me out or give me the answer. At least I'll have my book to teach me when it comes.. I don't know what else to say other than I have little to no math skills.

I seriously have no idea how to answer your question I like serena, and I don't want to frustrate you with my stupidity any longer lol... could you please give me a formula or even better the answer to the problem? It's just not in my mental capacity to be able to answer your question.

All I know is that the first book is 40m thick. I don't know what to do with the 2/5..

At this rate my homework will be due before I answer the 2nd question, haha.

 

[I like Serena]

... I really don't know. Like I've sat hwee for at least 2 hrs hoping someone could help me out or give me the answer. At least I'll have my book to teach me when it comes.. I don't know what else to say other than I have little to no math skills.

I seriously have no idea how to answer your question I like serena, and I don't want to frustrate you with my stupidity any longer lol... could you please give me a formula or even better the answer to the problem? It's just not in my mental capacity to be able to answer your question.

All I know is that the first book is 40m thick. I don't know what to do with the 2/5..

Well, if we start at page i of the first volume, and bore through the right of its cover of 1mm, it will take us 1mm to get through the cover.
If we then start at the second volume and bore through its cover of 1mm, it will take us another 1mm, at which time we'll arrive at the last page of the second volume.
That is, it takes 2 millimeters.
It's really a trick question, requiring us to visualize what is actually going on...

 

[jangoom]

42 from 1st page of volume one to the end of the first cover of volume two. The 2nd volume is 2/5 of the size of volime 1. What do I do with the 2/5 part?

Is there a policy saying you can't give me the answer or something? O-o

 

[I like Serena]

42 from 1st page of volume one to the end of the first cover of volume two. The 2nd volume is 2/5 of the size of volime 1. What do I do with the 2/5 part?

Is there a policy saying you can't give me the answer or something? O-o

No such thing. The 2/5 part is not relevant, nor is the 40 mm.
It's a trick question. It takes 2 millimeters, and it's not relevant at all how thick the volumes are - that is the answer!
The fact that 2/5 is given and that 40 mm is given, is only to confuse and distract.
Just put two volumes on a shelf and compare if you choose not to believe me.

 

[jangoom]

The answer was incorrect... it's not 42. I think you read the problem wrong. You can look at the picture provided..

I still have a friend that has the same question un answered, so if you or another could help me out.. or give me the answer to the 2nd question.

But 42 was incorrect.

 

[I like Serena]

The answer was incorrect... it's not 42. I think you read the problem wrong. You can look at the picture provided..

I still have a friend that has the same question un answered, so if you or another could help me out.. or give me the answer to the 2nd question.

But 42 was incorrect.

I said 2 and not 42... but if you choose not to believe me, let's just wait for someone else to corroborate...

Oh, and if someone does, or if you find that 2 is the correct answer, I think you owe me an apologee. (Worried)

 

[jangoom]

I submitted the wrong answer because I misunderstood you.. My bad. My friend told me you were right about it being 2 so thanks.

Think you can answer the 2nd question?

 

[I like Serena]

I submitted the wrong answer because I misunderstood you.. My bad. My friend told me you were right about it being 2 so thanks.

Think you can answer the 2nd question?

I literally repeated myself three times, and you chose to disbelieve me three times.
In my book three times is usually out.
Now you have to convince me why three times shouldn't be out. A proper apologee would help.
Of course you can wait for someone else who is more forgiving - I'm only just a volunteer after all.

 

[jangoom]

I don't understand. It's not that I didnt believe you.. I just didn't understand what the answer was dude. Like I said I have absolutely no math skills and you didn't really say, "2 is the answer." But I am sorry for being annoying, I did warn you that Id probably frustrate you. I was trying to learn how you got the answer, not question what you were saying... Sorry though.

So can you answer question 2 please? Or get someone to answer it for me? Thanks as you've been continually replying and answering me.

 

[Evgeny.Makarov]

For question 2, there is an obvious way to reach A: go left all the time. (By left I mean the viewer's left; for the driver that would be right.) Are there any other ways?

For B, the driver must go left 3 times and right 1 time. He/she may take the right turn at any of the four traffic directors along the left side of the triangle. So there are 4 ways to reach B.

There are 6 ways to reach C; I suggest finding them. For D and E I'll leave it to you as an exercise.

 

[HallsofIvy]

Well, if we start at page i of the first volume, and bore through the right of its cover of 1mm, it will take us 1mm to get through the cover.
If we then start at the second volume and bore through its cover of 1mm, it will take us another 1mm, at which time we'll arrive at the last page of the second volume.
That is, it takes 2 millimeters.
It's really a trick question, requiring us to visualize what is actually going on...

Why would "visualizing what is actually going on" be a "trick"? It is a pretty standard thing to do in any kind of problem solving. You seem to be saying that any question involving thinking rather than just putting numbers into a formula is a "trick question".