The problem is that strings are immutable. The methods replace, substring, etc. do not change the string itself. They create a new string and replace it. So for the above code to be correct, it should be
path1 = path.Replace("\\bin\\Debug", "\\Resource\\People\\VisitingFaculty.txt");
Or just
path = path.Replace("\\bin\\Debug", "\\Resource\\People\\VisitingFaculty.txt");
if another variable is not needed.
This answer is also a reminder that strings are immutable. Any change you make to them will in fact create a new string. So keep that in mind with everything that involves strings, including memory management.
As stated in the documentation here.
String objects are immutable: they cannot be changed after they have
been created. All of the String methods and C# operators that appear
to modify a string actually return the results in a new string object