time difference between 2 geographic coordinates The pre-calculus question was:
If it's 10 am in City A, $35.1667^{\circ}$S, $70.7^{\circ}$E, what time is it in city B at $24.3^{\circ}$S, $19.53^{\circ}$E.
I know that the time is based on longitude not latitude, so I found the difference between the 2 longitudes $70.7-19.53=51.17^{\circ}$. Since I know that there is $1$ hour of time difference for every $15^{\circ}$ of longitude I divided $51.17 $ by $15=3.41$ hours.  Since we were told it was ok to round, I rounded this to $3$ hours = $10-3= 7$am.
Book says $6$ am.  !!! So, I worked it the more accurate way of knowing that there is $4$ minutes of time difference for every $1 ^{\circ}$ of longitude. $51.17 * 4=204.68$ minutes.  This would indicate the same $3$ hours and $24$ mintues of time difference.  Technically, this would make it $6:36$ am in City B.  I don't see how I could possibly get $6$am unless I just drop the minutes entirely and NOT round.
Is there a proper way to do this problem, or is it subject to various methods of rounding/dropping?
 A: The prime meridian is, by definition in the middle of a time zone, typically denoted the +0 time zone since there is no time offset between that zone and itself.
Because $$5 \cdot 15^\circ - 7.5^\circ = 67.5^\circ < 70.7^\circ < 82.5^\circ = 5 \cdot 15^\circ + 7.5^\circ  \text{,}  $$ city A is in the +5 time zone east of the prime meridian.  Because $$1 \cdot 15^{\circ} - 7.5^\circ  = 7.5^\circ < 19.53^\circ < 22.5^\circ = 1 \cdot 15^\circ + 7.5^\circ  \text{,}  $$ city B is in the +1 timezone to the east of the prime meridian.  So in an ideal universe without national borders and seasonal time changes, there would be 4 hours time difference between the two cities.
However, in the real world, ...
City A is in the Indian ocean, further south than most of Australia, so this city's time zone is not complicated by national borders.  City B is in Namibia, so is actually in the Central Africa time zone, a +2 time zone.  (Namibia no longer implements Winter Time, so this UTC offset is correct year-round)  Accounting for this complication, the difference in times is 3 hours.
