This problem is similar in spirit to the notoriously tricky Burning Rope Problem. The key is to figure out how to use your two time-measuring devices in such a way that they compliment each other. You can see the original problem here.

Solution

Here is the first way to measure out 15 minutes:

  • Flip both the 11-minute and the 7-minute hourglasses over to start them both.
  • When the 7-minute hourglass runs out, that is the moment when you start to measure the target 15 minutes.
  • Four minutes after the 7-minute hourglass runs out, the 11-minute hourglass will run out.
  • Flip the 11-minute hourglass over immediately to measure another 11 minutes, landing you at 15 minutes exactly.

But there is a better way! The solution above requires 22 minutes, but it is possible to measure the 15 minutes in just 15 minutes without any wasted time. The second solution:

More From Popular Mechanics
 
preview for Popular Mechanics All Sections
  • Flip both the 11-minute and the 7-minute hourglasses over to start them both.
  • When the 7-minute hourglass runs out, flip it over immediately to restart it.
  • When the 11-minute hourglass runs out, flip the 7-minute hourglass over again, even though it is only partly finished.
  • When the 7-minute hourglass runs out, exactly 15 minutes have passed.

Let's take a moment to explain the second solution. You flip them both, and then when the 7-minute glass runs out, 7 minutes have passed. You flip the 7-minute glass over again to restart it. Then, four minutes later, the 11-minute hourglass runs out. That means the total time elapsed is 11 minutes. It also means that the 7-minute hourglass has 3 minutes remaining—and, it means that if you flip it over at that moment, there will be four minutes left until it runs out. Because 11 minutes have passed and the 7-minute hourglass will now measure out just four more minutes, you get exactly 15 minutes when it runs out.

Come back next week for another riddle!

*See all of our riddles here.

Headshot of Jay Bennett
Jay Bennett
Associate Editor


Jay Bennett is the associate editor of PopularMechanics.com. He has also written for Smithsonian, Popular Science and Outside Magazine.