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I would say that time exist and it doesn't exist. Time doesn't exist in nature but it does exist mathematically. Change is the reason for the birth of time. If there was no change, time would have never been INVENTED.
Change is natural and no one can deny that. When changes occur it occurs stage by stage, but when man came to think how long would that change last or what is the duration between one stage of the change to the other he found difficulty in expressing it and it was at that point that time came into play.
If a botanist did not want to know or tell what is the life duration of a plant or a tree etc he wouldn't need time, if a electrical engineer did not want to know for how long a bulb of particular power would glow he doesn't need time. So, time was invented in order to know the duration of change or the rate of change.
If one tells how fast a train goes from one station to the other then he actually expresses the change in the location of the train from one station to the other and in order to express that change he used time. Consider I'm buying an ups(uninterrupted power supply) I would want to know how long the charge in the battery of the ups would last when I do not have the power supply so what I do is I use time to tell the duration or the rate of change at which the batter would discharge its potential from full to zero and again to charge from zero to full.
So time arose only when we had the necessity to express the rate of change. I would say that time was invented for our convenience to express change. But then again this is just my personnel view.