conversions meters/kilometers

[guest612]

i'm having difficulty with what seems to be very basic. it's simple conversions and i just get stuck.
can you please help: 1) solve the problem 2) general rule/set up i can do so i don't get stuck? I even tried VICS but without the proper set up it was of no help

MBA Software question:

If the speed of x meters per second is equivalent to the speed of y kilometers per hour, what is y in terms of x? (1 kilometer = 1000 meters)

A. 5x/18
B. 6x/5
C. 18x/5
D. 60x
E. 3,600,000x

Answer is C. 18x/5

1) How do you get to answer C?
2) What is a general principle/set up formula I can use? I tried VICs AND basic ratio proportions and couldn't get there.

Many thanks!

[Sudhan]

I just tried converting the Kilometer to meter and seconds to hour to equate both the sides as follows:-

xm/3600 (per hr)= y*1000m (per hr)

Question is: y in terms of x

So rearranging and calculating both the sides

i am getting
y= x/3600000

I am not sure where I am missing here.

Pls correct me if I m wrong.

[RonPurewal]

here are 4 different ways to do this problem. the first is highly intuitive and highly specific to this type of problem (it capitalizes on the fact that both m/sec and km/h are easily modelled in the brain), but the other 3 are pretty general.

--

(1) think about these speeds in real life.

let x = 20.
let's say you're going 20 meters per second. that means that you can pass by a football field (soccer pitch, if you're not from the US) in about five to six seconds.
if you can drive by a football field (soccer pitch) in five to six seconds, then that means you're driving at a normal speed for a car on a city thoroughfare (imagine this in your head). that's around 40 miles per hour if you're american, which is around 65 kilometers per hour. (sorry americans, time to bone up on your metric units.)

plug x = 20 into the choices:
a = about 5.5 km/h
b = 24 km/h
c = 72 km/h
d = 1200 km/h
e = insane
the only one that comes close to our estimate is choice c, so, we'll take it.

--

(2) vic method
let x = 10, for no particularly good reason
then the speed is 10 meters per second.
because there are 3600 seconds in an hour, that's 10 x 3600 = 36,000 meters per hour.
but there are 1000 meters in a kilometer, so that's 36,000 / 1000 = 36 km/h.

plug x = 10 into the choices:
a = a lil under 3 km/h
b = 12 km/h
c = 36 km/h
d = 600 km/h
e = are you kidding?

answer = c

--

(3) use 'unit analysis' the same way you would in chemistry class. multiply by conversion factors, so that you can cancel the units you don't want and replace them with the units you do want.

here is a fairly good resource. it does the problem backwards, converting from km/h to m/s instead of the other way around, but the idea is the same.

--

(4) think about the way the units change. this is essentially the same approach taken to the vic method in (2) above, except no numbers are picked.

you have x meters per second. that means that you go x meters every second. how many meters do you go in an hour, then? dividing by 3600 makes no sense; we multiply by 3600, since it's x meters every second for 3600 seconds. therefore, you have 3600x meters per hour.

now, there are 1000 meters in a kilometer; a kilometer is bigger than a meter, so you have a smaller number of kilometers. that means 3600x meters per hour is 3600x / 1000 = 3.6x kilometers per hour. that's choice c.

[Sudhan]

Thanks Ron for your very detailed answer.

[guest612]

Ron, thanks for the detailed answer! That was very helpful! You rock.

[StaceyKoprince]

I'll also just add - whenever you have to convert from one unit to another, just set it up as a multiplication of fractions table. For the units you want to drop, make sure the "cancel out" until you're left only with the ones you want at the end.

eg let's say you've got 3 meters/hour and want to go to km/sec, just to switch things up a little (sorry about the dots - had to do it to get the formatting to line up correctly - those are supposed to be fractions)

3 meters * 1 km.. * 1 h.. * 1 min
1 hour.....1000 m....60 min...60 s

Try writing it out and then you just cross off corresponding units on top and bottom - it's like they're "dividing out." And you're left with what you want, which is km/s. Make sure that the units are where you want them, too - that is, km on the numerator and s on the denominator.

(This is good old dimensional analysis, which we learned way back in high school chemistry, if anybody cares. :)

[rkafc81]

Hi Stacey,

Sorry but I'm thoroughly confused with your reply... How does this work?

thanks!

[jnelson0612]

davy,
Let me show you a very simplified version of what Stacy is showing. This method is indeed something you probably learned in high school chemistry class.

For example, let's propose this problem:
If a car goes 2 hours at 50 miles per hour, how far will it go?

What we do is set it up so that units cross cancel on the top and bottom until we are left with the unit that we want. Here's how I do it:

50 miles X 2 hours = 100 miles
1 hour

Notice how we have units "hours" on the numerator and denominator of this problem. We can cross-cancel these two units, then the units we are left with is "miles", which correctly describes the numerical answer to this question, 100 miles.

This technique is used in chemistry class to help you multiply different units and eventually determine the answer in the units you want.

Please let me know if I can help further. Thank you,

[taniafconca]

Hi Stacey,

Would it be possible to clarify your conversion approach with regards to the gmat prep problem above...Im still confused!

Much appreciated.

Thank you
Tania

[StaceyKoprince]

Yes, but I can't show it here exactly the way we'd normally write it because the formatting doesn't work - and I think that's where the confusion is arising.

So grab a pen and paper and write this down yourself:


Now this problem also adds in the complication that we're dealing with variables, so let's simplify that and concentrate just on the conversion issue. If something is moving at 100 meters / second, then how many kilometers per hour is it going?

What's our starting point? 100 meters / second
What's our goal? ? kilometers / hour

given: 1 kilometer = 1000 meters
1 hour = 60 minutes
1 minute = 60 seconds

Write down the starting point as a fraction, with the words / labels (again, ignore the little dots - I have to use those to make the formatting come out correctly):
100 meters
......1 second

That's my starting point. Now, our goal is to change meters to kilometers and seconds to hours. How do we do that? Let's change from meters to kilometers first. There are 1000 meters in a kilometer. I need to write a fraction next to my first fraction - I'm going to multiply the two fractions together. That fraction will *either* be (1000 meters / 1 kilometer) OR (1 kilometer / 1000 meters). Which one? Well, I want to cancel out meters. In my first fraction, meters = the numerator. So, in my second fraction, I want to put meters on the bottom so that meters will cancel out.
100 meters * 1 kilometer
....1 second..............1000 meters

You know how you can cancel out numbers across the numerator and denominator? You can do the exact same thing with the labels! Cross off meters on the top and on the bottom. Now, we have kilometers / second.

Does that make more sense? As Jamie mentioned above, this might look familiar if you remember learning this in chemistry - this was a very common way to solve for things in chemistry.

Then, we want to go from seconds to hours. First, I have to go from seconds to minutes: 60 seconds per 1 minute. Again, I can write the fraction either (60 seconds / 1 minute) OR (1 minute / 60 seconds), depending upon what I want to cancel out. In this problem, seconds is on the bottom in the original number, so I want to put seconds on the top of my second fraction in order to cancel them out:
100 meters * 1 kilometer * 60 seconds
....1 second..............1000 meters........1 minute

Now we can cross off the word "second / seconds" on the top and bottom, and we're left with kilometers / minute.

And you can just keep doing this with any conversion until you go from what you were given to what you want to have in the end.

[taniafconca]

Great thank you!

[RonPurewal]

sure

[rachelhong2012]

I came to realize that conversion factor is just another way of expressing ratio.

Here,

x meter per second can be expressed as:
x meter : second

y kilometers per hour
y kilometers : 1 hour

One thing you should know is that when you multiply a ratio by a number, the essence of that ratio doesn't change. Meaning:

5 : 3
multiply this relationship/ratio by 2, we get:
10 : 6

they both mean the same thing, the ratio between 5:3 is the same as the ratio by 10:6, you can think of it as 5/3 is the same as 10/6.

Now going back to this problem:

x meters : seconds
y kilometers : 1 hour
the second expression can be rewritten as:
y kilometers: 60 x 60 seconds (which equals 1 hour)

furthermore, we know that 1 kilometer = 1000 meters
so we can rewrite it again as:

y 1000 meters: 3600 seconds

since this expression must be equivalent to

x meters : seconds
using the principle I explained a while ago, I want to make the second term comparable to the first one, so I multiple this expression by 3600

now it becomes:
3600 x meters : 3600 seconds

by doing so, I didn't change the "essence" of this ratio expression.

now this rewritten term:
3600 x meters : 3600 seconds

has thus become comparable to

y 1000 meters : 3600 seconds

since both stuffs on the left hand side are comparing to the same thing on the right hand side, I can compare them to each other directly. see the thing on the right hand side as a benchmark that both stuffs on the right hand side are being compared to.

so now I have
3600 x meters = y 1000 meters
rewrite it as y= something, work out the arithmetic and you will get
y = (3600 x) / 1000, or 18x/5


***

This approach seems pretty long when I write it, but it's very useful when you see a conversion problem next time. You don't have to worry about how to cancel out the units anymore, you just have to set it up like this, in ratio form. Which is easier to compare.

I took AP chem in high school and used to like the conversion factor approach but after trying to apply it to some unit conversion problems, it turned out to be more exhausting than I thought. usually took more than 2 minutes. Might just be that I'm not used to that kind of approach. I hope this approach helps those who aren't used to unit conversion approach

[tim]

good stuff. this idea is very helpful if a problem has units and you are comfortable dealing with units..