It's been too long

[Dave]

It has been to long since I have actually had to sit down and explain to a teacher of any sort how I actually come up with an Algebraic answer, and with that being said I have a Prof. that is asking me to explain how I would go about solving a few word problems the mathematical answer is not important just the process getting to the answer (a Logic's and Troubleshooting class). I'm hoping that if I can knock some of the cobwebs out of the old belfry that I can figure things out on my own.

Here is the first one that is stumping me: A construction crew has been asked to build a sidewalk around two sides of the City Hall building. The sidewalk is 110 meters from the north side, and 72 meters from the west side of the building. The outside of the sidewalk is 113.4 meters from the North side, and 75.4 meters from the west side. What is the area of the sidewalk?

Any help would be greatly appreciated, I just can't quite seem to get a starting point to work off of that makes sense.

If I am looking at this correctly what I need to do is figure out the length of both the North and West sides then everything should be pretty basic from there. My question is what formula would I use to find to find either one of those lengths as I'm at a loss right now?

 

[HallsofIvy]

It has been to long since I have actually had to sit down and explain to a teacher of any sort how I actually come up with an Algebraic answer, and with that being said I have a Prof. that is asking me to explain how I would go about solving a few word problems the mathematical answer is not important just the process getting to the answer (a Logic's and Troubleshooting class). I'm hoping that if I can knock some of the cobwebs out of the old belfry that I can figure things out on my own.

Here is the first one that is stumping me: A construction crew has been asked to build a sidewalk around two sides of the City Hall building. The sidewalk is 110 meters from the north side, and 72 meters from the west side of the building. The outside of the sidewalk is 113.4 meters from the North side, and 75.4 meters from the west side. What is the area of the sidewalk?

Any help would be greatly appreciated, I just can't quite seem to get a starting point to work off of that makes sense.

If I am looking at this correctly what I need to do is figure out the length of both the North and West sides then everything should be pretty basic from there. My question is what formula would I use to find to find either one of those lengths as I'm at a loss right now?

Start by drawing a picture. However, I don't see how that can be done without knowing the size of the building. The length of the "sidewalk on the north side of the building" depends on the length of the north side of the building and the length of the "sidewalk on the west side of the building" depends on the length of the west side of the buiding.

 

[mmm4444bot]

Halls is correct. The best that you can do is to provide a symbolic answer; that is, describe the solution process using symbols (eg: N for building's north length, W for building's west length).

Are you able to visualize the two segments of sidewalk? I had to draw a labeled diagram. Can you determine the sidewalk width, from the given information? That basic subtraction step is something that you'll need to describe in your answer, yes? Do you remember the formula for the area of a rectangle? (Each segment of sidewalk is a rectangle.)

I added the phrase in red below, as that's how I'm interpreting the given information.

The inside of the sidewalk is 110 meters from the north side, and 72 meters from the west side of the building. The outside of the sidewalk is 113.4 meters from the North side, and 75.4 meters from the west side. What is the area of the sidewalk?

If you need help drawing a diagram, let us know.

 

[mmm4444bot]

OR:
The inside of the sidewalk is 110 meters from the north side, and 72 meters from the west side of the building. The width of the sidewalk is 3.4 meters. What is the area of the sidewalk?

This would generate a different algorithm. The steps need to begin with the given information, and I believe that changing the given information is not a valid step.

 

[mmm4444bot]

This is a logics and troubleshooting course, and the exercise asks for an algorithm (not an area value).

I'm fairly certain that one of the steps needs to be a calculation of the sidewalk width using subtraction.

If you change the given information to include the sidewalk width, then the subtraction step drops out of the algorithm, and you're working a different exercise.

Analogy: Write computer program for end-user to generate area from given inputs.

Your first step is to change the assignment parameters so that the end-user now needs to enter the sidewalk width instead of having the program generate it from the given inputs.

You would not get full credit from me. Capish ?

 

[mmm4444bot]

I would be honored to have had you hire me in the first place.

Really, I think that the OP needs to include a description of the width calculation. Just sayin'.

 

[mmm4444bot]

Good grief. I might post camera-ready copy for the given exercise. It will be an algorithm with no explicitly-written formulas, equations, or Real-numbered calculations whatsoever (i.e., just the following).

to explain how I would go about solving

mathematical answer is not important

just the process

Again, this exercise does not come from a traditional math course.

 

[mmm4444bot]

[Calculating the sidewalk's width] is of course a necessary part of finding a solution

Finding a solution is not a part of this exercise.

If I were debugging code that was not giving the correct answer, I'd start by looking at the length logic, not the width logic.

There is no code, in this exercise. The analogy that I provided is only an example to help Denis understand that changing the given information leads to description of a different process.

 

[mmm4444bot]

There is another ambiguity in this problem as it has been presented.

From my point-of-view, there is no ambiguity. I drew a labeled diagram, and linear thinking did the rest. In the absence of feedback from the OP, I will eventually post an answer to this exercise.

As far as second-guessing or different interpretations perceived, one is always free to cover all of their bases!

I see this exercise as a test of linear thinking abilities and common-sense knowledge.

 

[mmm4444bot]

I am completely confused as to why asserting the obvious conclusion that the width of the sidewalk is 3.4 meters materially changes the problem.

I agree. You are completely confused over my point. :cool:

surely the main point of the exercise is describe how to find the length of the sidewalk

Your interpretation of this exercise is different than mine. :cool:



PS: The nuns help me finish any leftovers

 

[mmm4444bot]

but my point here is

Sorry to say, I do not understand the pronoun above.

Your first point is to suggest changing the given information (or some type of abbreviation of the given information). Is that "shortcut" the point which you reference above?

If you are referencing some other type of endeavor, then I ​probably agree with your rhetorical below :cool:; otherwise, the statement below makes little sense to me because the student only needs to state the algorithm once for the exercise in this thread.

So why use (113.4 - 110) everytime a calculation involving sidewalk's width is required?

 

[mmm4444bot]

Well, I can't do no better than this:

Width of sidewalk is evidently 3.4

< insert loud-buzzer sound here >

:twisted: