We hang one of the ropes perfectly vertical, wait for the North Star to be out, so we can position the other rope pointing perfectly north, and then we have a makeshift sundial. The following day, assuming it's not overcast we can put some graduations around our sundial, and calculate 45 minutes.
The lighter is there to help us see what we're doing whilst tying the ropes up in the dark.
Good trick question Mr. Spendur. Give us a hard one next time!