How can you measure time without using a stopwatch? You could use the movement of the Sun across the sky, watch a pendulum swing, or burn some very special string. Keep on reading to find out how it works!
How to Solve It — Step 1
Instead of lighting just one end of a piece of string on fire, we start by lighting both ends on fire at the same time.
Here’s what we need to do: Instead of lighting just one end of a piece of string on fire, we start by lighting both ends on fire at the same time. What does this do for us? Well, the uneven thickness of a piece of string means that we can't say how fast the fire will move at any given moment as it's burning from one end to the other (or the other way around). But, nonetheless, we do know that the two flames burning towards each other must come together and meet (although we’re not quite sure where) after precisely 30 minutes! Make sense?
That means we now have a way to measure 30 minute intervals in addition to 1 hour intervals. Of course, what we really want is to measure a time interval of 45 minutes. So we’re not done yet. What do we do now? Before answering that question, once again if you haven’t figured it out yet, I encourage you to stop for a minute and think about it before continuing on.
How to Solve It — Step 2
OK, so what can we do to measure a 45 minute time interval instead of just 30 or 60 minute time intervals? The trick is that right after we simultaneously light that first string from both ends, we need to light another string from only one end. Then, when the two flames of the first string come together—which we've already figured out marks the 30 minute point—we need to light the other end of the now half-burned (in terms of time) second string. At this point, the two flames of the second string will start burning towards each other, and they will meet in the middle after exactly another 15 minutes pass.
Putting all of this together, we see that the burning ends of the second string must meet a total of 30 + 15 or 45 minutes after we started this whole process of setting strings on fire. And thus, by applying a bit of clever thinking, we have managed to measure a time interval of 45 minutes. Pretty cool, right?
OK, that’s all the math puzzling we have time for today.
For more fun with math, please check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of The Math Dude on Facebook, where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.
Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!
Burning fuse image from Shutterstock.