The Jailhouse

[Mark Marcellus]

Okay, I can't stand letting this hang

Start one candle burning at both ends and the other at one end. When the first candle burns out, light the other end of the second one.

Note that this is not 100% certain to be correct, but it's the best I can do in 20 minutes. You have to assume that, whatever the variation in rates, lighting at both ends will halve the burn time at whatever point in time you choose to do it. Since the method is "mysterious" (and especially since measurement is of no use) there is no way of being sure it will.