My university has a co-op program, so I applied for the position on the co-op website.

I was invited to do a 30-minute panel interview. The panel consisted of two interviewers: an HR representative and a Software Programmer.

The interview was broken down for me at the start into three phases:

• The first part was about me. They asked me to talk about myself, my strengths and weaknesses, my extracurricular activities, past employment, etc. It was basically me talking about myself for 10 minutes with a few prompts from them.
• This was followed by the logic portion. They asked me two logic questions so they could see what my thought process was like. One was the rope-burning question (given two ropes and a lighter + some additional knowledge, how would you determine when 45 minutes have passed?) and one was about how to determine the number of camels used for transportation in Egypt. They gave me some hints for the rope-burning problem and plenty of time.
• The interview concluded with about 5-8 minutes for me to ask them any questions I had.

I received an offer 8 days later.

You are given two ropes of equal length and a lighter. If you light a rope at one end, it takes an hour for it to completely burn, but it does not burn at a constant rate. For example, the first quarter of the rope might take 50 minutes to burn, and the remaining three quarters might only take 10 minutes.

Using this knowledge, how would you figure out when 45 minutes have passed?