Burning Time

Apr 07, 2008

RAY: This was submitted by Paco Jain and it's from my Space and Time Series, though it had nothing to do with space, and just a little bit to do with time. Here it is:

Do you remember those old Westerns on TV where the bad guys would try to blast the door off the bank vault with dynamite? They would strategically locate the explosives and then light a fuse, which had a long enough burn time to allow them to get a safe distance away before the blast? Well this is about those kinds of fuses.

Imagine that you have two lengths of fuse like that and each takes exactly 1 hour to burn. But the fuses don't burn evenly and they're both likely to be different. So let's say a fuse is 1 foot long and it takes 40 minutes for the first inch to burn and then only 20 minutes for next 11 inches to burn. Or it could be 12 minutes for the first 4 inches and 48 minutes for the last 8 inches to burn. All you know is that the fuses are not identical and that they each take 1 hour to burn completely.

Now using only these two fuses and a cigarette lighter, how do you measure 45 minutes?
RAY: Well here's the answer. You light three ends at the same time, or as close to the same time as you possibly can. So you light two ends of one fuse and one end of the other fuse.

When the first fuse, the one whose both ends are lit, has completely burned up, that's half an hour. Because if it took an hour for it to burn from A to B, one end to the other end, if you light both ends the whole fuse will be consumed in half an hour.

TOM: Yeah.

RAY: OK. In the meantime that other fuse has been burning. If, as soon as the first fuse has burned up completely, you light the last end. So you've used up half an hour, and now it takes another 15 minutes for the new end to catch up to the original lit end and voila!

TOM: Boy, that is very good.

RAY: Do we have a winner?

TOM: The winner this week is Becky Salon from Lunenburg, Vermont. And for having her answer selected at random from the pile of correct answers that we got, Becky is going to get a 26-dollar gift certificate to the Shameless Commerce Division at cartalk.com, with which Becky can get one of our sleek looking (not really) black, red, gray and white baseball jerseys.

RAY: Congratulations, Becky!

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