If you light both ends of one rope, it will burn
in exactly a 1/2 hour. Thus, burn one rope from both ends and the
other rope from only one end. Once the one rope (which is burning
from both ends) finally burns out (and you know a 1/2 hour has
elapsed), you also know that the other rope (which is buring from
only one end) has exactly 1/2 hour left to burn. Since you only
want 45 minutes, light the second end of the rope. This remaining
piece will burn in 15 minutes. Thus, totaling 45
minutes.