There are two stops that are 2 kilometers away from each other. What is the distance between the next two stops on a map with a scale of 2 centimeters : 1 kilom

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Answer 1

^{Hi Person from Kouts, IN.  :-)}

 

This might be a trick question.  :-)  Without knowing what the "next two stops" they're talking about, it's hard to answer the problem.  

 

However, I think it's a pretty safe bet to assume they're just looking at scale factors, which is really just a particular type of conversion factor.

 

All conversion factors are really just fractions that describe the same thing divided by itself in different forms, so you can change from one form to another.  Any time you divide something by itself, no matter if they look different, you always end up with a big fat 1.  What's more, you can multiply and divide by 1 all day long and still be left with the exact same thing you started with, (although perhaps in disguise).  In this case, they've given us 2cm(map):1km(real).  (I'm distinguishing because they are being measured different places, so we have to treat them as different things.)

 

So since 2cm(map) is equivalent to 1km(real), we could say:

 

2cm(map)   or...   1km(real)        ...and they would both equal the same giant 1 in disguise.

1km(real)            2cm(map)

 

So we just have to figure out what we started with and where we want to end up in order to figure out which one we want to use.  They both actually mean the exact same thing, the only difference is the form.

 

In this problem, we started with 2km(real), and we want to convert that into cm(map).

 

So, start with what we have:  (Starting thing always goes on top.  If it's not already a fraction, just put it over 1!)

 

START:

 

2km(real)

     1

 

I'm going to take it and multiply it by one of our conversion factors, but I'm going to make sure I pick the one that cancels out the thing I don't want anymore (km(real)), and leaves the thing I do want on top.

 

So I need the conversion factor with km(real) on bottom, (opposite the original), and cm(map) on top.

 

That's 2cm(map)
          1km(real)  

 

So if we start with                    and multiply it by 

 

2 km(real)                *                  2cm(map)
    1                                            1km(real)

 

The km(real)s in top and bottom both cancel, and you're left with:

 

2                             *                 2cm(map)                     =                4cm(map).

 

Let us know if you have any questions!!  We're here to help!  :-)

 

-Ellen M.