How can I know the time difference between two cities almost at the same latitude?

Question

Well I know that's the earth rotation speed is:

$v=1669.756481\frac{km}{h}$

I have two cities New York, Madrid almost at the same latitude and the distance between them is:

$d=5774.39$ $km$

I know that's :

$\Delta t=\frac{d}{v}=3.4582$ $hours$ --> +3:27

But after I calculated it I found it wrong (according to http://www.timeanddate.com/worldclock/) and (http://www.happyzebra.com/timezones-worldclock/difference-between-New%20York-and-Madrid.php) time difference = +6:00 ???!!!

Answer 1

Speed of the earth at equator is equal to $1669.756481$ km/h. Speed of the earth at latitude of $40.400$ degrees equals

$$ 1669.756481 \cos\left(40.400\right )\,km/h $$

Answer 2

I think that you have to take not the real distance between the two cities but the projected distance on the equator. That is the distance between the points of intersection of the meridian of New York and the equator and of the meridian of Madrid and the equator. This because the velocity of rotation of earth of 1669 km/h is taken at equator.

In more details:

Longitudes of New York and Madrid are 78°51' W and 3°41' W so the difference is approximately of 75° (see here).

The Earth's circumference at the equator is 40075.017 km, so the distance between two principal meridians is of

$\frac{40075.017\ \text{km}}{360} = 111.32\ \text{km}$

If you multiply this quantity for 75° that is the difference in longitude between New York and Madrid you get the distance of these two cities projected at the equator:

$111.32\ \text{km} \cdot 75 = 8348.96\ \text{km}$

so

$\Delta t = \frac{8348.96\ \text{km}}{1669.756481\ \text{km}/\text{h}} = 5\ \text{h}$

But Madrid is not in the time zone corresponding to its position but in the Europe Central one so this add an hour giving exactly 6 hours.