I believe this solution is also possible .. Please comment ...
1. Ignite the first cord at the two ends and somewhere approximately in the middle so that the fire from the middle propagates towards the two ends. It should take 15 minutes for this first cord to burn out completely (There would be two pieces of the first igniter cord since it was ignited at the middle as well - EVERY LAST BIT should burn out)
2. Ignite at the second cord at the two ends as soon as the first cord "completely" burns out. This would take another 30 minutes.
This would not be an accurate measurement. If the cords burned at constant speed throughout the whole cord, and you started at exactly the center, this would be fine, but this is not the case in the rules.
Even though you're trying to start one at the approx. middle, you might get differing times. One might burn up in 12 and the other 18. Without thinking too hard on it, the average would probably be 15 minutes, but even then, we cannot measure something on averages.