There would be a time where you would constantly ask every person you have encountered how near the summit is.
The sentence is in the form where I constantly observe people in every climbing asking about the distance of the summit.
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I think you may be mixing your tenses.
Your sentence seems to be giving advice to someone who is considering a climb in the future, and as they get closer to the top
There will be a time when you will constantly be asking every person you encounter how close the summit is.
Stylistically, I might change it to
There will come a time when you will ask every person you come across how far it is to the summit.
If you wanted to place your original sentence it in the past, as if the climber used to do this
There was a time when you would constantly ask every person you had encountered how near the summit was.
which might imply they may no longer do this since they are more experienced.