You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different.
How do you measure 45 minutes?
Burn one string from both ends, it will vanish in 1/2 hr. At the same time, burn other string at one end.
Once first string has burned completely, burn the second string at other end as well. It will take 15 minutes (in additional to first 30 minutes) for second string to completely burn.