If 2 pieces of string take 1 hour to burn how do you know when 3 quarters of an hour is up?

Answer 1

"First, you light both ends of one of the strings until it burns out. Then you light the second string on both ends and in the exact middle. The first string will take exactly 30 minutes to burn and the second one will take 15"

I agree with the first part. If the string does not burn evenly, it will take 30 mins for both lit ends to meet. If not, then one would take longer than the other to meet which is impossible. Hence 30 minutes are up once the 1st string is gone.

Now consider simply lighting the 2nd string in the middle...

Who's to say that THAT particular half of the string does not simply burn up in 1 min and the other remaining half in 29mins?

To conduct this accurately, one would need four lighters and triggers to set them off.

Set alight to both ends of string number 1 whilst simultaneously setting alight one end of string number 2.

Once the first string has burnt out after exactly 30 minutes, you know that there is '30 mins of string left' on string 2. Hence, one can apply procedure 1 onto the second string by lighting the unlit end, and the time it would take for both ends to meet is exactly half of 30, i.e. 15 mins, as explained above. Add the two together, hey presto!