Well I know that's the earth speed is:
$v=1669.756481\frac{km}{h}$
and I have two cities Moscow and NewYork the distance between them is:
$d=7518.92$ $km$
Actually I know that's :
$\Delta t=\frac{d}{v}$
But the distance in this case is a arc distance not a straight also the cities aren't at the same latitude distance look at this photo :

So how can I calculate the time difference $\Delta t$ between them in case like this ?
What you need is the arc distance (I am assuming by arc you mean the shortest distance on the surface of earth). Assuming that they are at the same latitude then it will take the earth $\frac{5576.74km}{1669.756481km/h}= 3.33985229 $ hours.
This is wrong for a bunch of reasons. These are the two I can think of.
The speed you gave for the earth is at the Equator.(http://image.gsfc.nasa.gov/poetry/ask/a10840.html) >