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!

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.

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

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(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.

Thanks Ron for your very detailed answer.

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

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. :)