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Zaman and Vakit  are same --> Time  

Süre is more specific ,it is believed that this word is derived of  a turkish verb stem "sür". To operate. To operate a horse, as we know that Turks were nomad in Middle Asia and they were always operating their horses , I mean riding the horses. For example; to operate a horse ---> at sürmek .  So, after it took the suffix ´a [e]´ and  it changed into a noun süre which  as a noun referred as  "the period of time of operating an event. [operating the horse in those times] but at present time anything"  DURATION

In other words, the period of time from its starting point and its finish point which is duration.

Ne kadar zamandır ----> For how long ? [asking how long as in time ] 

Ne kadar vakittir   ----> Same

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 Example 1: Ne kadar zamandır gebesin? ---> Since how long have you been pregnant ? 

Example 2: Ne kadar süre yüzebiliriz?   ---> How long can we swim ?

 in other words, how long we would be able to swim , how long  could we swim , how long time will pass between from our  starting time and our finishing time ?

Example 3: İtalya´da ne kadar kalacaksınız? [zaman/süre not needed in this case?]  ---> NO , zaman or süre is not needed. 

Question: When exactly does one use (n)either of them?